ncert-solutions-class-7-maths-ch-12-algebraic-expressions

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions

NCERT solutions for class 7 maths chapter 12 algebraic expressions topic 12.2

Question: Describe how the following expressions are obtained:

$7xy+5, x^{2} y,4x^{2}-5x$

Answer:

the above expression is obtained by adding 7xy with 5. Here 7xy is obtained by multiplying 7,x and y

the above expression is obtained by subtracting the product of 5 and x from the product of 4,x and x

NCERT solutions for class 7 maths chapter 12 algebraic expressions topic 12.3

Question:1 What are the terms in the following expressions? Show how the terms are formed. Draw a tree diagram for each expression:

$8y+3x^{2},7mn-4,2x^{2}y.$

Answer:

$8y+3x^{2}$ The terms in the expression are

$8y\ and\ 3x^{2}$

$8y+3x^{2}$ is obtained by adding the product of 8 and y with the product of 3 x and x

the tree diagram for the expression is given below

has two terms 7mn and 4 and the expression is obtained by subtracting 4 from the product of 7,m and n. The tree diagram is shown below.

has only one term, that is the expression itself.

The expression is formed by multiplying 4 terms 2, x, x and y. The tree diagrams are shown below

Question:2 Write three expressions each having 4 terms.

Answer:

We can write as many expressions we need with 4 terms. Following are a few examples of expression with 4 terms

$\\ a+b+c+d\\ab+bc+cd+ad\\abc+bcd+acd+abcd$

Question: Identify the coefficients of the terms of following expressions:

Answer:

i) has two terms 4x and -3y

the coefficient of x is 4 and the coefficient of y is -3

ii) a+b+5 has 3 terms a,b and a constant that is 5.

the coefficient of a is 1 and b is also 1. Constant terms have no coefficient

iii) 2y+5 has two terms 2y and 5 which is constant.

The coefficient of y is 2. Constant terms have no coefficient

iv) 2xy has only one term which is 2xy and the coefficient of xy is 2

NCERT solutions for class 7 maths chapter 12 algebraic expressions topic 12.4

Question:1(i) Group the like terms together from the following:

, , , , , , , ,

Answer:

The like terms are grouped below

Group 1: , ,

Group 2: , ,

Group 3: , ,

NCERT solutions for class 7 maths chapter 12 algebraic expressions topic 12.5 monomials, binomials, trinomials and polynomials

Question: Classify the following expressions as a monomial, a binomial or a trinomial:

$a,a+b.ab+a+b,ab+a+b-5,xy,xy+5,5x^{2}-x+2,4pq-3q+5p,7,4m-7n+10,4mn+7.$

Answer:

Monomial: a, xy, 7

binomial: a+b, xy+5, 4mn+7

Trinomial: ab+a+b, 5x 2 -x+2, 4pq-3q+5p, 4m-7n+10

Polynomial with 4 terms: ab+a+b-5

NCERT solutions for class 7 maths chapter 12 algebraic expression exercise 12.1

Question: 1(i) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

Subtraction of from .

Answer:

Subtraction of z from y:

Question: 1(ii) Get the algebraic expressions in the following cases using variables, constants and arithmetic operation.

One-half of the sum of numbers and .

Answer:

Sum of numbers x and y = x + y

One half of the sum of numbers x and y

$=\frac{x+y}{2}$

Question: 1(iii) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

The number multiplied by itself.

Answer:

The number multiplied by itself $=z\times z=z^{2}$

Question: 1(iv) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

One-fourth of the product of numbers and .

Answer:

Product of the numbers p and q $= p \times q=pq$

One-fourth of the product of numbers p and q

$=\frac{pq}{4}$

Question: 1(v) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

Numbers and both squared and added.

Answer:

Number x squared = $x^{2}$

Number y squared = $y^{2}$

Numbers x and y both squared and added = $x^{2}+ y^{2}$

Question:1(vi) Get the algebraic expressions in the following cases using variables, constants and arithmetic operation.

Number 5 added to three times the product of numbers and .

Answer:

Product of numbers m and n $=m\times n=mn$

Number 5 added to three times the product of numbers <img alt="m" height="8"

src="https://lh5.googleusercontent.com/arsc1mpklCs1n8qiYZvtHNPm9fa0uetvmhCBZorSJj2Ya9f0INlu4t15ELtdSaZ57cpEU_Sp7u6umzMIo-BziIxsePoZEyiCNz799vmlgzwjl0sU8Pl_Yb64eSNBpQErxPXBPJA" style="margin-left: 0px; margin-top: 0px;" width="16" /> and = $=3\times mn+5=3mn+5$

Question:1(vii) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

Product of numbers and subtracted from .

Answer:

Product of numbers y and z $=y\times z=yz$

Product of numbers y and z subtracted from 10

Question: 1(viii) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

Sum of numbers and subtracted from their product.

Answer:

Sum of numbers a and b = a + b

Product of the numbers a and b $=a\times b=ab$

Sum of numbers and subtracted from their product .

Question:2(i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams. (a)

Answer:

Expression : x - 3

Terms in the above expression: x and -3

Tree diagram for the given expression

Question: 2 (i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams (b) $1+x+x^{2}$

Answer:

Expression:

Tems in the above expression: $1, x \and\ x^2$

Factors of x 2 : x and x

Tree diagram for the given expression

Question:2(i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams (c) $y-y^{3}$

Answer:

Expression: y - y 3

Tems in the above expression: y and -y 3

Factors of -y 3 : -1, y, y and y

Tree diagram for the given expression

Question: 2 (i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams. (d) $5xy^{2}+7x^{2}y$

Answer:

Expression: 5xy 2 + 7x 2 y

Terms in the above expression: 5xy 2 and 7x 2 y

Factors of 5xy 2 : 5, x, y and y

Factors of 7x 2 y: 7, x, x and y

Tree diagram for the given expression

Question: 2 (i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams (e) $-ab+2ab^{2}-3a^{2}$

Answer:

Expression: -ab + 2ab 2 - 3a 2

Terms in the above expression: -ab, 2ab 2 and -3a 2

Factors of -ab: -1, a and b

Factors of 2ab 2 : 2, a, b and b

Factors of -3a 2 : -1, 3, a and a

Tree diagram for the given expression

Question: 2 (ii) Identify terms and factors in the expressions given below:

(a)

Answer:

Expression: -4x + 5

Terms in the above expression: -4x and 5

Factors of -4x: -1, 4 and x

Factors of 5: 5

Question: 2 (ii) Identify terms and factors in the expressions given below:

(b)

Answer:

Expression: -4x + 5y

Terms in the above expression: -4x and 5y

Factors of -4x: -1, 4 and x

Factors of 5y: 5 and y

Question: 2 (ii) Identify terms and factors in the expressions given below:

Answer:

Expression: 5y + 3y 2

Terms in the above expression: 5y and 3y 2

Factors of 5y: 5 and y

Factors of 3y 2 : 3, y and y

Question: 2 (ii) Identify terms and factors in the expressions given below:

(d) $xy+2x^{2}y^{2}$

Answer:

Expression: xy + 2x 2 y 2

Terms in the above expression: xy and 2x 2 y 2

Factors of xy: x and y

Factors of 2x 2 y 2 : 2, x, x, y and y

Question: 2 (ii) Identify terms and factors in the expressions given below:

(e)

Answer:

Expression: pq + q

Tems in the above expression: pq and q

Factors of pq: p and q

Factors of q: q

Question: 2 (ii) Identify terms and factors in the expressions given below:

(f) $1.2 \; ab-2.4\; b+3.6\; a$

Answer:

Expression: 1.2ab - 2.4b + 3.6a

Tems in the above expression: 1.2ab, -2.4b and 3.6a

Factors of 1.2ab: 1.2, a and b

Factors of -2.4b: -1, 2.4 and b

Factors of 3.6a: 3.6 and a

Question: 2( ii) Identify terms and factors in the expressions given below:

(g) $\frac{3}{4}x+\frac{1}{4}$

Answer:

Expression: $\frac{3}{4}x+\frac{1}{4}$

Terms in the above expression: $\frac{3}{4}x$ and $\frac{1}{4}$

Factors of $\frac{3}{4}x$ : $\frac{3}{4}$ and x

Factors of $\frac{1}{4}$ : $\frac{1}{4}$

Question: 2 (ii) Identify terms and factors in the expressions given below:

(h) $0.1\; p^{2}+0.2\; q^{2}$

Answer:

Expression: 0.1p 2 + 0.2q 2

Tems in the above expression:0.1p 2 and 0.2q 2

Factors of 0.1p 2 : 0.1, p and p

Factors of 0.2q 2 : 0.2, q and q

Question:3(i) Identify the numerical coefficients of terms (other than constants) in the following expressions:

$5-3t^{2}$

Answer:

Expression: 5 - 3t 2

Tems in the above expression: 5 and -3t 2

Coefficient of -3t 2 : -3

Question:3(ii) Identify the numerical coefficients of terms (other than constants) in the following expressions:

$1+t+t^{2}+t^{3}$

Answer:

Expression: 1 + t + t 2 + t 3

Terms in the above expression: 1, t, t 2 and t 3

Coefficient of t is 1

Coefficient of t 2 is 1

Coefficient of t 3 : is 1

Question: 3(iii) Identify the numerical coefficients of terms (other than constants) in the following expressions:

Answer:

Expression: x + 2xy + 3y

Terms in the above expression: x, 2xy and 3y

Coefficient of x: 1

Coefficient of 2xy: 2

Coefficient of 3y: 3

Question: 3(iv) Identify the numerical coefficients of terms (other than constants) in the following expressions:

Answer:

Expression: 100m + 1000n

Terms in the above expression: 100m and 1000n

Coefficient of 100m: 100

Coefficient of 1000n: 1000

Question: 3(v) Identify the numerical coefficients of terms (other than constants) in the following expressions:

$-p^{2}q^{2}+7pq$

Answer:

Expression: -p 2 q 2 + 7pq

Tems in the above expression: -p 2 q 2 and 7pq

Coefficient of -p 2 q 2 : -1

Coefficient of 7pq: 7

Question:3(vi) Identify the numerical coefficients of terms (other than constants) in the following expressions:

$1.2\; a+0.8\; b$

Answer:

Expression: 1.2a + 0.8b

Terms in the above expression: 1.2a and 0.8b

Coefficient of 1.2a: 1.2

Coefficient of 0.8b: 0.8

Question:3(vii) Identify the numerical coefficients of terms (other than constants) in the following expressions:

$3.14\; r^{2}$

Answer:

Expression: 3.14r 2

Terms in the above expression: 3.14r 2

Coefficient of 3.14r 2 is 3.1

Question: 3(viii) Identify the numerical coefficients of terms (other than constants) in the following expressions:

Answer:

Expression: 2(l + b) = 2l + 2b

Tems in the above expression: 2l and 2b

Coefficient of 2l: 2

Coefficient of 2b: 2

Question: 3(ix) Identify the numerical coefficients of terms (other than constants) in the following expressions:

$0.1\; y+0.01\; y^{2}$

Answer:

Expression: 0.1y + 0.01y 2

Tems in the above expression: 0.1y and 0.01y 2

Coefficient of 0.1y is 0.1

Coefficient of 0.01y 2 is 0.01

Question: 4 (a) Identify terms which contain x and give the coefficient of x.

(i) $y^{2}x+y$

Answer:

Expression: y 2 x + y

Terms with x: y 2 x

Coefficient of x in y 2 x: y 2

Question:4(a) Identify terms which contain x and give the coefficient of x.

(ii) $13y^{2}-8yx$

Answer:

Expression: 13y 2 - 8yx

Terms with x: -8yx

Coefficient of x in -8yx: -8y

Question: 4 (a) Identify terms which contain x and give the coefficient of x.

(iii)

Answer:

Expression: x + y + 2

Terms with x: x

Coefficient of x in x: 1

Question: 4 (a) Identify terms which contain x and give the coefficient of x.

(iv)

Answer:

Expression: 5 + z + zx

Terms with x: zx

Coefficient of x in zx: z

Question: 4 (a) Identify terms which contain x and give the coefficient of x .

(v)

Answer:

Expression: 1 + x + xy

Terms with x: x and xy

Coefficient of x in x: 1

Coefficient of x in xy: y

Question:4(a) Identify terms which contain x and give the coefficient of x.

(vi) $12xy^{2}+25$

Answer:

Expression: 12xy 2 + 5

Terms with x: 12xy 2

Coefficient of x in 12xy 2 : 12y 2

Question:4(a) Identify terms which contain x and give the coefficient of x.

(vii) $7x+xy^{2}$

Answer:

Expression: 7x + xy 2

Terms with x: 7x and xy 2

Coefficient of x in 7x: 7

Coefficient of x in xy 2 : y 2

Question: 4 (b) Identify terms which contain $y^{2}$ and give the coefficient of $y^{2}$ .

(i) $8-xy^{2}$

Answer:

Expression: 8 - xy 2

Terms with y 2 : -xy 2

Coefficient of y 2 in -xy 2 : -x

Question: 4 (b) Identify terms which contain $y^{2}$ and give the coefficient of $y^{2}$ .

(ii) $5y^{2}+7x$

Answer:

Expression: 5y 2 + 7x

Terms with y 2 : 5y 2

Coefficient of y 2 in 5y 2 : 5

Question: 4 (b) Identify terms which contain $y^{2}$ and give the coefficient of $y^{2}$ .

(iii) $2x^{2}y-15xy^{2}+7y^{2}$

Answer:

Expression: 2x 2 y -15xy 2 + 7y 2

Terms with y 2 : -15xy 2 and 7y 2

Coefficient of y 2 in -15xy 2 : -15x

Coefficient of y 2 in 7y 2 : 7

Question:5 Classify into monomials, binomials and trinomials.

(i) 4y – 7z

(ii) y 2

(iii) x + y – xy

(iv) 100

(v) ab – a – b

(vi) 5 – 3t

(vii) 4p 2 q – 4pq 2

(viii) 7mn

(ix) z 2 – 3z + 8

(x) a 2 + b 2

(xi) z 2 + z

(xii) 1 + x + x 2

Answer:

(i) 4y – 7z

Binomial

(ii) y 2

Monomial

(iii) x + y – xy

Trinomial

(iv) 100

Monomial

(v) ab – a – b

Trinomial

(vi) 5 – 3t

Binomial

(vii) 4p 2 q – 4pq 2

Binomial

(viii) 7mn

Monomial

(ix) z 2 – 3z + 8

Trinomial

(x) a 2 + b 2

Binomial

(xi) z 2 + z

Binomial

(xii) 1 + x + x 2

Trinomial

Question:6(i) State whether a given pair of terms is of like or unlike terms.

Answer:

(i) are Like terms.

Question:6(ii) State whether a given pair of terms is of like or unlike terms.

$-7x,\frac{5}{2}x$

Answer:

(ii) $-7x,\frac{5}{2}x$ are Like terms

Question:6(iii) State whether a given pair of terms is of like or unlike terms.

Answer:

Unlike since y and x are unlike terms

Question: 6(iv) State whether a given pair of terms is of like or unlike terms.

Answer:

like terms since both the terms contain xy and only the coefficient is different

Question: 6(v) State whether a given pair of terms is of like or unlike terms.

$4m^{2}p,4mp^{2}$

Answer:

Unlike since $m^2p \ and \ mp^2$ are different

Question: 6(vi) State whether a given pair of terms is of like or unlike terms.

$12xz,12x^{2}z^{2}$

Answer:

Unlike since $xz \ and\ x^2z$ are unlike terms

Question:7(a) Identify like terms in the following:

$-xy^{2},-4yx^{2},8x^{2},2xy^{2},7y,-11x^{2},-100x,-11yx,20x^{2}y,-6x^{2},y,2xy,3x$

Answer:

Like terms are

(i) -xy 2 and 2xy 2

(ii) -4x 2 y and 20x 2 y

(iii) 8x 2 , -11x 2 and -6x 2

(iv) 7y and y

(v) -100x and 3x

(vi) -11yx and 2xy

Question:7(b) Identify like terms in the following:

<img alt="10pq,7p,8q,-p^{2}q^{2},-7qp,-100q,-23,12q^{2}p^{2},-5p^{2},41,2405p,78qp,13p^{2}q,qp^{2},701p^{2}" height="20"

src="https://lh5.googleusercontent.com/UJ2iRhFqVFmcYal3807co9nCJyVc08bNHsGuRySpSDNqir3PPnoNpJON8NJ6GTJm1l0F7LK1Zo9M3tIlzE3iEDTabfpW5IGiGfSsn7TCldXKRrPaUWq8sLVNegPyqTocnzW_g_I" style="margin-left: 0px; margin-top: 0px;" width="648" />

Answer:

Like terms are

(i) 10pq, -7qp and 78qp

(ii) 7p and 2405p

(iii) 8q and -100q

(iv) -p 2 q 2 and 12q 2 p 2

(vii) -23 and 41

(viii) -5p 2 and 701p 2

(ix) 13p 2 q and qp 2

NCERT solutions for class 7 maths chapter 12 algebraic expressions topic 12.6

Question:(i) Add and subtract

Answer:

Adding

Will give the result as follows

Subtracting

Will give the result as follows

Question:(ii) Add and subtract

Answer:

adding the following terms

we will get

Subtracting

We will get

NCERT solutions for class 7 maths chapter 12 algebraic expression exercise: 12.2

Question: 1(i) Simplify combining like terms:

Answer:

21b - 32 + 7b -20b

= (21 + 7 - 20)b -32

= 8b - 32

The simplified expression is 8b - 32.

Question:1(ii) Simplify combining like terms:

$-z^{2}+13z^{2}-5z+7z^{3}-15z$

Answer:

$-z^{2}+13z^{2}-5z+7z^{3}-15z$

-z 2 + 13z 2 - 5z + 7z 3 - 15z

= (-1 + 13)z 2 + (-5 - 15)z +7z 3

=12z 2 - 20z + 7z 3

The simplified expression is 12z 2 - 20z + 7z 3

Question:1(iii) Simplify combining like terms:

Answer:

p - (p - q) - q - (q - p)

= p - p + q - q - q + p

= p - p + p + q - q -q

= p - q

The simplified expression is p - q.

Question: 1(iv) Simplify combining like terms:

Answer:

3a - 2b - ab - (a - b + ab) + 3ab + b - a

= 3a - 2b - ab - a + b - ab + 3ab + b - a

= (3 - 1 - 1)a + (-2 + 1 +1)b + (-1 - 1 + 3)ab

= a + ab

The simplified expression is a + ab.

Question:1(v) Simplify combining like terms:

$5x^{2}y-5x^{2}+3yx^{2}-3y^{2}+x^{2}-y^{2}+8xy^{2}-3y^{2}$

Answer:

5x 2 y - 5x 2 + 3yx 2 - 3y 2 + x 2 - y 2 + 8xy 2 - 3y 2

= (5 + 3 )x 2 y + (-5 + 1)x 2 + (-3 - 1 - 3)y 2 + 8xy 2

= 8x 2 y - 4x 2 - 7y 2 + 8xy 2

The simplified expression is 8x 2 y - 4x 2 - 7y 2 + 8xy 2

Question:1(vi) Simplify combining like terms:

$(3y^{2}+5y-4)-(8y-y^{2}-4)$

Answer:

(3y 2 + 5y - 4) - (8y - y 2 - 4)

= 3y 2 + 5y - 4 - 8y + y 2 + 4

= (3 + 1)y 2 + (5 - 8)y - 4 + 4

= 4y 2 - 3y

The simplified expression is 4y 2 - 3y

Question:2 Add:

(i)

(ii)

(iii)

(iv)

(v)

vi)

(vii) $4x^{2}y,-3xy^{2},-5xy^{2},5x^{2}y$

(viii) $3p^{2}q^{2}-4pq+5,-10 p^{2}q^{2},15+9pq+7p^{2}q^{2}$

(ix)

(x) $x^{2}-y^{2}-1,y^{2}-1-x^{2},1-x^{2}-y^{2}$

Answer:

The given terms are added as follows

$\\(i) 3mn + (-5mn) + 8mn + (-4mn)\\ = (3 - 5 + 8 - 4)mn\\ = 2mn$

$\\(vii) 4x^2y - 3xy^2 - 5xy^2 + 5x^2y\\ \\= (4 + 5)x^2y + (-3 - 5)xy^2 \\= 9x^2y - 8xy^2$

Question:3 Subtract:

(i) $-5y^{2}$ from $y^{2}$

(ii) from

(iii) from

(iv) from

(v) $-m^{2}+5mn$ from $4m^{2}-3mn+8$

(vi) $-x^{2}+10x-5$ from

(vii) $5a^{2}-7ab+5b^{2}$ from $3ab-2a^{2}-2b^{2}$

(viii) $4pq-5q^{2}-3p^{2}$ from $5p^{2}+3q^{2}-pq$

Answer:

The given terms are subtracted as follows

(i)

$\\ y^2 - (-5y^2) \\= y^2 + 5y^2 \\= 6y^2$

(ii)

$\\ -12xy - 6xy\\ = -18xy$

(iii)

$\\(a+b)-(a-b)\\ =a+b-a+b =2b$

(iv)

$\\ b(5 - a) - a(b - 5) \\= 5b - ab - (ab - 5a) \\= 5b - ab - ab + 5a \\= 5b - 2ab + 5a$

(v)

(vi)

(vii)

(viii)

Question: 4 (a) What should be added to $x^{2}+xy+y^{2}$ to obtain

$2x^{2}+3xy?$

Answer:

Let the term be a which must be added to x 2 + xy + y 2 to obtain 2x 2 + 3xy

x 2 + 2xy - y 2 should be added to x 2 + xy + y 2 to obtain 2x 2 + 3xy

Question: 4 (b) What should be subtracted from to get

Answer:

Let the term be c which must be subtracted from 2a + 8b + 10 to get -3a + 7b + 16

5a + b - 6 must be subtracted from 2a + 8b + 10 to get -3a + 7b + 16

Question: 5 What should be taken away from $3x^{2}-4y^{2}+5xy+20$ to obtain

$-x^{2}-y^{2}+6xy+20 ?$

Answer:

Let the term be a which must be taken away from 3x 2 - 4y 2 + 5xy + 20 to obtain -x 2 - y 2 + 6xy + 20

4x 2 - 3y 2 - xy must be taken away from 3x 2 - 4y 2 + 5xy + 20 to obtain -x 2 - y 2 + 6xy + 20

Question:6(a) From the sum of and , subtract

Answer:

On subtracting 3x - y - 11 from the sum of 3x - y + 11 and -y - 11 we get -y + 11

Question: 6 (b) From the sum of and $5-4x+2x^{2},$ subtract the sum of $3x^{2}-5x$ and $-x^{2}+2x+5$ .

Answer:

On subtracting the sum of $3x^{2}-5x$ and $-x^{2}+2x+5$ from the sum of and $5-4x+2x^{2}$ we get

NCERT solutions for class 7 maths chapter 12 algebraic expression exercise 12.3

Question:1(i) If find the value of:

Answer:

(i) m - 2

= 2 - 2

= 0

If m = 2 the value of m - 2 = 0

Question:1(ii) If find the value of:

Answer:

$\\3m - 5 \\= 3 \times 2 - 5 \\= 6 - 5 \\= 1$

If m = 2 the value of 3m - 5 = 1

Question:1(iii) If find the value of:

Answer:

$\\9 - 5m \\= 9 - 5 \times 2 \\= 9 - 10 \\= -1$

If m = 2 the value of 9 - 5m = -1

Question: 1(iv) If find the value of:

$3m^{2}-2m-7$

Answer:

$\\3m^2 - 2m - 7 \\= 3 \times 2^2 - 2 \times 2 - 7 \\= 12 - 4 - 7 \\= 1$

If m = 2 the value of 3m 2 - 2m - 7 = 1

Question: 1(v) If find the value of: (v) If find the value of:

$\frac{5m}{2}-4$

Answer:

$\frac{5m}{2}-4$

$=\frac{5\times 2}{2}-4$

= 5 - 4

= 1

If m = 2 the value of $\frac{5m}{2}-4 = 1$

Question:2(i) If find the value of:

Answer:

$\\4p + 7 \\= 4 \times ( -2 ) + 7 \\= -8 + 7 \\= -1$

If p = -2 the value of 4p + 7 = -1

Question: 2(ii) If find the value of:

$-3p^{2}+4p+7$

Answer:

$\\-3p^2 + 4p + 7 \\= -3 x ( -2 )^2 + 4 x ( -2 ) + 7 \\= -12 - 8 + 7 \\= -13$

If p = -2 the value of -3p 2 + 4p + 7 = -13

Question: 2(iii) If , find the value of:

$-2p^{3}-3p^{2}+4p+7$

Answer:

If p = -2 the value of -2p 3 - 3p 2 + 4p + 7 = 3

Question: 3(i) Find the value of the following expressions, when :

Answer:

$\\2x - 7 \\= 2 \times ( -1 ) - 7 \\= -2 - 7 \\= -9$

If x = -1 the value of 2x - 7 = -9

Question: 3(ii) Find the value of the following expressions, when

Answer:

-x + 2

= -( -1 ) + 2

= 1 + 2

= 3

If x = -1 the value of -x + 2 = 3

Question:3(iii) Find the value of the following expressions, when :

$x^{2}+2x+1$

Answer:

$\\x^2 + 2x + 1 \\= ( -1 )^2 + 2 \times ( -1 ) + 1 \\= 1 - 2 + 2 \\= 0$

If x = -1 the value of x 2 + 2x + 1 = 0

Question:3(iv) Find the value of the following expressions, when :

$2x^{2}-x-2$

Answer:

$\\2x^2 - x - 2 \\= 2\times ( -1 )^2 - ( -1 ) - 2 \\ = 2 + 1 - 2 \\= 1$

So the value at x=-1 is 1

Question: 4(i) If find the value of:

$a^{2}+b^{2}$

Answer:

a 2 + b 2

= ( 2 ) 2 + ( -2 ) 2

= 4 + 4

= 8

If a = 2 and b = -2 the value of a 2 + b 2 = 8

Question: 4(ii) If find the value of:

$a^{2}+ab+b^{2}$

Answer:

$\\a^2 + ab + b^2 \\= 2^2 + 2 \times ( -2 ) + ( -2 )^2 \\= 4 - 4 + 4 \\= 4$

If a = 2 and b = -2 the value of a 2 + ab + b 2 = 4

Question:4(iii) If <img alt="a=2,b=-2," height="17"

src="https://lh4.googleusercontent.com/jkGQZTyeHgoQl56RQVl1rjkfUV_eLp8SXZZfcmIVjGsMUdCvAGUCBSqI4OL9tUsZbXeMUCdgbybvEj8xe4sJrCH4vF9QpfGHq8WKrHxfPuDiKZlO3EgdICYzLOdmZ01QKgRGqL8" style="margin-left: 0px; margin-top: 0px;" width="109" /> find the value of

$a^{2}-b^{2}$

Answer:

a 2 - b 2

= 2 2 - ( -2 ) 2

= 4 - 4

= 0

If a = 2 and b = -2 the value of a 2 - b 2 = 0

Question: 5(i) When find the value of the given expressions:

Answer:

$\\2a + 2b \\= 2 \times 0 + 2 \times ( -1 ) \\= 0 - 2 \\= -2$

When a = 0 and b = -1 the value of the given expression 2a + 2b = -2

Question: 5(ii) When find the value of the given expressions:

$2a^{2}+b^{2}+1$

Answer:

$\\2a^2 + b^2 + 1 \\= 2 \times 0^2 + ( -1 )2 + 1 \\= 0 + 1 + 1 \\= 2$

When a = 0 and b = -1 the value of the given expression 2a 2 + b 2 + 1 = 2

Question: 5(iii) When , find the value of the given expressions:

$2a^{2}b+2ab^{2}+ab$

Answer:

When a = 0 and b = -1 the value of the given expression 2a 2 b + 2ab 2 + ab = 0

Question:5(iv) When find the value of the given expressions:

$a^{2}+ab+2$

Answer:

$\\a^2 + ab + 2 \\= 0^2 + 0 \times ( -1 ) + 2 \\= 0 + 0 + 2 \\= 2$

When a = 0 and b = -1 the value of the given expression a 2 + ab + 2 = 2

Question: 6(i) Simplify the expressions and find the value if is equal to

Answer:

$\\x + 7 + 4( x - 5 ) \\= x + 7 + 4x - 20 \\= 5x - 13 \\= 5 \times 2 - 13 \\= 10 - 13 \\= -3$

If x is equal to 2 the value of x + 7 + 4( x - 5 ) = -3

Question: 6(ii) Simplify the expressions and find the value if is equal to

Answer:

$\\3( x + 2 ) + 5x - 7 \\= 3x + 6 + 5x - 7 \\= 8x - 1 \\= 8 \times (2) - 1 \\= 16 - 1 \\= 15$

If x is equal to 2 the value of 3( x + 2 ) + 5x - 7 = 15

Question: 6(iii) Simplify the expressions and find the value if is equal to

Answer:

$\\6x + 5( x - 2 ) \\= 6x + 5x - 10 \\= 11x - 10 \\= 11 \times 2 - 10 \\= 22 - 10 \\= 12$

If x is equal to 2 the value of 6x + 5( x - 2 ) = 12

Question: 6(iv) Simplify the expressions and find the value if is equal to

Answer:

$\\4( 2x - 1 ) + 3x + 11 \\= 8x - 4 + 3x + 11 \\= 11x + 7 \\= 11 \times 2 + 7 \\= 22 + 7 \\= 29$

If x is equal to 2 the value of 4( 2x - 1 ) + 3x + 11 = 29

Question: 7 Simplify these expressions and find their values if

(i)

(ii)

(iii)

(iv)

(v)

Answer:

The expression is simplified as follows and also obtained their values

(i)

$\\ 3x - 5 - x + 9 \\= 2x + 4 \\= 2 \times 3 + 4 \\= 10$

(ii)

$\\ 2 - 8x + 4x + 4 \\= 6 - 4x \\= 6 - 4 \times 3 \\= -6$

(iii)

$\\3a + 5 - 8a + 1 \\= -5a + 6 \\= -5 \times ( -1 ) + 6 \\= 5 + 6 \\=11$

(iv)

$\\10 - 3b - 4 - 5b \\= 6 - 8b \\= 6 - 8 \times ( -2 ) \\= 6 + 16 \\= 22$

(v)

Question: 8 (i) If find the value of

$z^{3}-3(z-10)$

Answer:

$\\z^3 - 3( z - 10 ) \\= z^3 - 3z + 30 \\= 10^3 - 3 \times 10 + 30 \\= 1000 - 30 + 30 \\= 1000$

If z = 10 the value of z 3 - 3( z - 10 ) = 1000

Question: 8 (ii) If find the value of

$p^{2}-2p-100$

Answer:

$\\p^2 - 2p - 100 \\= ( -10 )^2 - 2 \times ( -10 ) - 100 \\= 100 + 20 - 100 \\= 20$

If p = -10 the value of p 2 - 2p - 100 = 20

Question: 9 What should be the value of a if the value of $2x^{2}+x-a$ equals to , when

Answer:

$\\2x^2 + x - a = 5 \\2 \times 0^2 + 0 - a = 5 \\-a = 5 \\a = -5$

Therefore for a = -5 when the value of x=0

Question: 10 Simplify the expression and find its value when and

$b=-3\; .2(a^{2}+ab)+3-ab$

Answer:

When a = 5 and b = -3 the value 2( a 2 + ab ) + 3 - ab = 38

NCERT solutions for class 7 maths chapter 12 algebraic expression exercise 12.4

Question:1 Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.

If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern. How many segments are required to form 5, 10, 100 digits of the kind

Answer:

The number of segments required to form n of each digits shown above are 5n + 1, 3n + 1 and 5n + 2

When n = 5

$\\5n + 1 = 5 \times 5 + 1 = 26 \\3n + 1 = 3 \times 5 + 1 = 16 \\5n + 2 = 5 \times 5 + 2 = 27$

When n = 10

$\\5n + 1 = 5 \times 10 + 1 = 51 \\3n + 1 = 3 \times 10+ 1 = 31 \\5n + 2 = 5 \times 10 + 2 = 52$

When n = 100

$\\5n + 1 = 5 \times 100 + 1 = 501 \\3n + 1 = 3 \times 100+ 1 = 301 \\5n + 2 = 5 \times 100 + 2 = 502$

Question: 2 Use the given algebraic expression to complete the table of number patterns.

Answer:

Below you can find the table of number patterns:

Responsive Table

Chapter No.Chapter Name

Chapter 1	NCERT solutions for class 7 maths chapter 1 Integers
Chapter 2	NCERT solutions for class 7 maths chapter 2 Fractions and Decimals
Chapter 3	NCERT solutions for class 7 maths chapter 3 Data Handling
Chapter 4	NCERT solutions for class 7 maths chapter 4 Simple Equations
Chapter 5	NCERT solutions for class 7 maths chapter 5 Lines and Angles
Chapter 6	NCERT solutions for class 7 maths chapter 6 The Triangle and its Properties
Chapter 7	NCERT solutions for class 7 maths chapter 7 Congruence of Triangles
Chapter 8	NCERT solutions for class 7 maths chapter 8 comparing quantities
Chapter 9	NCERT solutions for class 7 maths chapter 9 Rational Numbers
Chapter 10	NCERT solutions for class 7 maths chapter 10 Practical Geometry
Chapter 11	NCERT solutions for class 7 maths chapter 11 Perimeter and Area
Chapter 12	NCERT solutions for class 7 maths chapter 12 Algebraic Expressions
Chapter 13	NCERT solutions for class 7 maths chapter 13 Exponents and Powers
Chapter 14	NCERT solutions for class 7 maths chapter 14 Symmetry
Chapter 15	NCERT solutions for class 7 maths chapter 15 visualising-solid-shapes

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NCERT solutions for class 7 maths chapter 12 algebraic expressions topic 12.2

NCERT solutions for class 7 maths chapter 12 algebraic expressions topic 12.3

NCERT solutions for class 7 maths chapter 12 algebraic expressions topic 12.4

NCERT solutions for class 7 maths chapter 12 algebraic expressions topic 12.5 monomials, binomials, trinomials and polynomials

NCERT solutions for class 7 maths chapter 12 algebraic expression exercise 12.1

NCERT solutions for class 7 maths chapter 12 algebraic expressions topic 12.6

NCERT solutions for class 7 maths chapter 12 algebraic expression exercise: 12.2

NCERT solutions for class 7 maths chapter 12 algebraic expression exercise 12.3

NCERT solutions for class 7 maths chapter 12 algebraic expression exercise 12.4

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