# NCERT Solutions for Class 7 Maths Exercise 12.2 Chapter 12 Algebraic Expressions

NCERT Solutions for Class 7 Maths Exercise 12.2 Chapter 12 Algebraic Expressions in simple PDF are available here. Adding and subtracting like terms and adding and subtracting general algebraic expressions are the two topics covered in this exercise of NCERT Solutions for Class 7 Maths Chapter 12. Subject experts prepare these solutions for algebraic expressions to help students for their exam preparations. Students can either practise online or download these NCERT Solutions for Class 7 Maths and practise different types of questions.

## Download the PDF of NCERT Solutions For Class 7 Maths Chapter 12 Perimeter and Area â€“ Exercise 12.2

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### Access Other Exercises of NCERT Solutions For Class 7 Maths Chapter 12 â€“ Algebraic Expressions

Exercise 12.1 Solutions

Exercise 12.3 Solutions

Exercise 12.4 Solutions

### Access Answers to NCERT Solutions for Class 7 Maths Chapter 12 â€“ Algebraic Expressions Exercise 12.2

1. Simplify combining like terms:

(i) 21b â€“ 32 + 7b â€“ 20b

Solution:-

When term have the same algebraic factors, they are like terms.

Then,

= (21b + 7b â€“ 20b) â€“ 32

= b (21 + 7 â€“ 20) â€“ 32

= b (28 â€“ 20) â€“ 32

= b (8) â€“ 32

= 8b â€“ 32

(ii) â€“ z2 + 13z2 â€“ 5z + 7z3 â€“ 15z

Solution:-

When term have the same algebraic factors, they are like terms.

Then,

= 7z3 + (-z2 + 13z2) + (-5z â€“ 15z)

= 7z3 + z2 (-1 + 13) + z (-5 â€“ 15)

= 7z3 + z2 (12) + z (-20)

= 7z3 + 12z2 â€“ 20z

(iii) p â€“ (p â€“ q) â€“ q â€“ (q â€“ p)

Solution:-

When term have the same algebraic factors, they are like terms.

Then,

= p â€“ p + q â€“ q â€“ q + p

= p â€“ q

(iv) 3a â€“ 2b â€“ ab â€“ (a â€“ b + ab) + 3ab + b â€“ a

Solution:-

When term have the same algebraic factors, they are like terms.

Then,

= 3a â€“ 2b â€“ ab â€“ a + b â€“ ab + 3ab + b â€“ a

= 3a â€“ a â€“ a â€“ 2b + b + b â€“ ab â€“ ab + 3ab

= a (1 â€“ 1- 1) + b (-2 + 1 + 1) + ab (-1 -1 + 3)

= a (1 â€“ 2) + b (-2 + 2) + ab (-2 + 3)

= a (1) + b (0) + ab (1)

= a + ab

(v) 5x2y â€“ 5x2 + 3yx2 â€“ 3y2 + x2 â€“ y2 + 8xy2 â€“ 3y2

Solution:-

When term have the same algebraic factors, they are like terms.

Then,

= 5x2y + 3yx2 â€“ 5x2 + x2 â€“ 3y2 â€“ y2 â€“ 3y2

= x2y (5 + 3) + x2 (- 5 + 1) + y2 (-3 â€“ 1 -3) + 8xy2

= x2y (8) + x2 (-4) + y2 (-7) + 8xy2

= 8x2y â€“ 4x2 â€“ 7y2 + 8xy2

(vi) (3y2 + 5y â€“ 4) â€“ (8y â€“ y2 â€“ 4)

Solution:-

When term have the same algebraic factors, they are like terms.

Then,

= 3y2 + 5y â€“ 4 â€“ 8y + y2 + 4

= 3y2 + y2 + 5y â€“ 8y â€“ 4 + 4

= y2 (3 + 1) + y (5 â€“ 8) + (-4 + 4)

= y2 (4) + y (-3) + (0)

= 4y2 â€“ 3y

2. Add:

(i) 3mn, â€“ 5mn, 8mn, â€“ 4mn

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to add the like terms

= 3mn + (-5mn) + 8mn + (- 4mn)

= 3mn â€“ 5mn + 8mn â€“ 4mn

= mn (3 â€“ 5 + 8 â€“ 4)

= mn (11 â€“ 9)

= mn (2)

= 2mn

(ii) t â€“ 8tz, 3tz â€“ z, z â€“ t

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to add the like terms

= t â€“ 8tz + (3tz â€“ z) + (z â€“ t)

= t â€“ 8tz + 3tz â€“ z + z â€“ t

= t â€“ t â€“ 8tz + 3tz â€“ z + z

= t (1 â€“ 1) + tz (- 8 + 3) + z (-1 + 1)

= t (0) + tz (- 5) + z (0)

= â€“ 5tz

(iii) â€“ 7mn + 5, 12mn + 2, 9mn â€“ 8, â€“ 2mn â€“ 3

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to add the like terms

= â€“ 7mn + 5 + 12mn + 2 + (9mn â€“ 8) + (- 2mn â€“ 3)

= â€“ 7mn + 5 + 12mn + 2 + 9mn â€“ 8 â€“ 2mn â€“ 3

= â€“ 7mn + 12mn + 9mn â€“ 2mn + 5 + 2 â€“ 8 â€“ 3

= mn (-7 + 12 + 9 â€“ 2) + (5 + 2 â€“ 8 â€“ 3)

= mn (- 9 + 21) + (7 â€“ 11)

= mn (12) â€“ 4

= 12mn â€“ 4

(iv) a + b â€“ 3, b â€“ a + 3, a â€“ b + 3

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to add the like terms

= a + b â€“ 3 + (b â€“ a + 3) + (a â€“ b + 3)

= a + b â€“ 3 + b â€“ a + 3 + a â€“ b + 3

= a â€“ a + a + b + b â€“ b â€“ 3 + 3 + 3

= a (1 â€“ 1 + 1) + b (1 + 1 â€“ 1) + (-3 + 3 + 3)

= a (2 -1) + b (2 -1) + (-3 + 6)

= a (1) + b (1) + (3)

= a + b + 3

(v) 14x + 10y â€“ 12xy â€“ 13, 18 â€“ 7x â€“ 10y + 8xy, 4xy

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to add the like terms

= 14x + 10y â€“ 12xy â€“ 13 + (18 â€“ 7x â€“ 10y + 8xy) + 4xy

= 14x + 10y â€“ 12xy â€“ 13 + 18 â€“ 7x â€“ 10y + 8xy + 4xy

= 14x â€“ 7x + 10yâ€“ 10y â€“ 12xy + 8xy + 4xy â€“ 13 + 18

= x (14 â€“ 7) + y (10 â€“ 10) + xy(-12 + 8 + 4) + (-13 + 18)

= x (7) + y (0) + xy(0) + (5)

= 7x + 5

(vi) 5m â€“ 7n, 3n â€“ 4m + 2, 2m â€“ 3mn â€“ 5

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to add the like terms

= 5m â€“ 7n + (3n â€“ 4m + 2) + (2m â€“ 3mn â€“ 5)

= 5m â€“ 7n + 3n â€“ 4m + 2 + 2m â€“ 3mn â€“ 5

= 5m â€“ 4m + 2m â€“ 7n + 3n â€“ 3mn + 2 â€“ 5

= m (5 â€“ 4 + 2) + n (-7 + 3) â€“ 3mn + (2 â€“ 5)

= m (3) + n (-4) â€“ 3mn + (-3)

= 3m â€“ 4n â€“ 3mn â€“ 3

(vii) 4x2y, â€“ 3xy2, â€“5xy2, 5x2y

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to add the like terms

= 4x2y + (-3xy2) + (-5xy2) + 5x2y

= 4x2y + 5x2y â€“ 3xy2 â€“ 5xy2

= x2y (4 + 5) + xy2 (-3 â€“ 5)

= x2y (9) + xy2 (- 8)

= 9x2y â€“ 8xy2

(viii) 3p2q2 â€“ 4pq + 5, â€“ 10 p2q2, 15 + 9pq + 7p2q2

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to add the like terms

= 3p2q2 â€“ 4pq + 5 + (- 10p2q2) + 15 + 9pq + 7p2q2

= 3p2q2 â€“ 10p2q2 + 7p2q2 â€“ 4pq + 9pq + 5 + 15

= p2q2 (3 -10 + 7) + pq (-4 + 9) + (5 + 15)

= p2q2 (0) + pq (5) + 20

= 5pq + 20

(ix) ab â€“ 4a, 4b â€“ ab, 4a â€“ 4b

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to add the like terms

= ab â€“ 4a + (4b â€“ ab) + (4a â€“ 4b)

= ab â€“ 4a + 4b â€“ ab + 4a â€“ 4b

= ab â€“ ab â€“ 4a + 4a + 4b â€“ 4b

= ab (1 -1) + a (4 â€“ 4) + b (4 â€“ 4)

= ab (0) + a (0) + b (0)

= 0

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(x) x2 â€“ y2 â€“ 1, y2 â€“ 1 â€“ x2, 1 â€“ x2 â€“ y2

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to add the like terms

= x2 â€“ y2 â€“ 1 + (y2 â€“ 1 â€“ x2) + (1 â€“ x2 â€“ y2)

= x2 â€“ y2 â€“ 1 + y2 â€“ 1 â€“ x2 + 1 â€“ x2 â€“ y2

= x2 â€“ x2 â€“ x2 â€“ y2 + y2 â€“ y2 â€“ 1 â€“ 1 + 1

= x2 (1 â€“ 1- 1) + y2 (-1 + 1 â€“ 1) + (-1 -1 + 1)

= x2 (1 â€“ 2) + y2Â (-2 +1) + (-2 + 1)

= x2 (-1) + y2Â (-1) + (-1)

= -x2 â€“ y2 -1

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3. Subtract:

(i) â€“5y2 from y2

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to subtract the like terms

= y2 â€“ (-5y2)

= y2Â + 5y2

= 6y2

(ii) 6xy from â€“12xy

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to subtract the like terms

= -12xy â€“ 6xy

= â€“ 18xy

(iii) (a â€“ b) from (a + b)

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to subtract the like terms

= (a + b) â€“ (a â€“ b)

= a + b â€“ a + b

= a â€“ a + b + b

= a (1 â€“ 1) + b (1 + 1)

= a (0) + b (2)

= 2b

(iv) a (b â€“ 5) from b (5 â€“ a)

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to subtract the like terms

= b (5 -a) â€“ a (b â€“ 5)

= 5b â€“ ab â€“ ab + 5a

= 5b + ab (-1 -1) + 5a

= 5a + 5b â€“ 2ab

(v) â€“m2 + 5mn from 4m2 â€“ 3mn + 8

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to subtract the like terms

= 4m2 â€“ 3mn + 8 â€“ (- m2 + 5mn)

= 4m2 â€“ 3mn + 8 + m2 â€“ 5mn

= 4m2 + m2 â€“ 3mn â€“ 5mn + 8

= 5m2 â€“ 8mn + 8

(vi) â€“ x2 + 10x â€“ 5 from 5x â€“ 10

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to subtract the like terms

= 5x â€“ 10 â€“ (-x2 + 10x â€“ 5)

= 5x â€“ 10 + x2 â€“ 10x + 5

= x2 + 5x â€“ 10x â€“ 10 + 5

= x2 â€“ 5x â€“ 5

(vii) 5a2 â€“ 7ab + 5b2 from 3ab â€“ 2a2 â€“ 2b2

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to subtract the like terms

= 3ab â€“ 2a2 â€“ 2b2 â€“ (5a2 â€“ 7ab + 5b2)

= 3ab â€“ 2a2 â€“ 2b2 â€“ 5a2 + 7ab â€“ 5b2

= 3ab + 7ab â€“ 2a2 â€“ 5a2 â€“ 2b2 â€“ 5b2

= 10ab â€“ 7a2 â€“ 7b2

(viii) 4pq â€“ 5q2 â€“ 3p2 from 5p2 + 3q2 â€“ pq

Solution:-

When term have the same algebraic factors, they are like terms.

Then, we have to subtract the like terms

= 5p2 + 3q2 â€“ pq â€“ (4pq â€“ 5q2 â€“ 3p2)

= 5p2 + 3q2 â€“ pq â€“ 4pq + 5q2 + 3p2

= 5p2 + 3p2 + 3q2 + 5q2 â€“ pq â€“ 4pq

= 8p2 + 8q2 â€“ 5pq

4. (a) What should be added to x2 + xy + y2 to obtain 2x2 + 3xy?

Solution:-

Let us assume p be the required term

Then,

p + (x2 + xy + y2) = 2x2 + 3xy

p = (2x2Â + 3xy) â€“ (x2 + xy + y2)

p = 2x2 + 3xy â€“ x2 â€“ xy â€“ y2

p = 2x2 â€“ x2 + 3xy â€“ xy â€“ y2

p = x2Â + 2xy â€“ y2

(b) What should be subtracted from 2a + 8b + 10 to get â€“ 3a + 7b + 16?

Solution:-

Let us assume x be the required term

Then,

2a + 8b + 10 â€“ x = -3a + 7b + 16

x = (2a + 8b + 10) â€“ (-3a + 7b + 16)

x = 2a + 8b + 10 + 3a â€“ 7b â€“ 16

x = 2a + 3a + 8b â€“ 7b + 10 â€“ 16

x = 5a + b â€“ 6

5. What should be taken away from 3x2 â€“ 4y2 + 5xy + 20 to obtain â€“ x2 â€“ y2 + 6xy + 20?

Solution:-

Let us assume a be the required term

Then,

3x2 â€“ 4y2 + 5xy + 20 â€“ a = -x2 â€“ y2 + 6xy + 20

a = 3x2 â€“ 4y2 + 5xy + 20 â€“ (-x2 â€“ y2 + 6xy + 20)

a = 3x2 â€“ 4y2 + 5xy + 20 + x2 + y2 â€“ 6xy â€“ 20

a = 3x2 + x2 â€“ 4y2 + y2 + 5xy â€“ 6xy + 20 â€“ 20

a = 4x2 â€“ 3y2 â€“ xy

6. (a) From the sum of 3x â€“ y + 11 and â€“ y â€“ 11, subtract 3x â€“ y â€“ 11.

Solution:-

First we have to find out the sum of 3x â€“ y + 11 and â€“ y â€“ 11

= 3x â€“ y + 11 + (-y â€“ 11)

= 3x â€“ y + 11 â€“ y â€“ 11

= 3x â€“ y â€“ y + 11 â€“ 11

= 3x â€“ 2y

Now, subtract 3x â€“ y â€“ 11 from 3x â€“ 2y

= 3x â€“ 2y â€“ (3x â€“ y â€“ 11)

= 3x â€“ 2y â€“ 3x + y + 11

= 3x â€“ 3x â€“ 2y + y + 11

= -y + 11

(b) From the sum of 4 + 3x and 5 â€“ 4x + 2x2, subtract the sum of 3x2 â€“ 5x and

â€“x2 + 2x + 5.

Solution:-

First we have to find out the sum of 4 + 3x and 5 â€“ 4x + 2x2

= 4 + 3x + (5 â€“ 4x + 2x2)

= 4 + 3x + 5 â€“ 4x + 2x2

= 4 + 5 + 3x â€“ 4x + 2x2

= 9 â€“ x + 2x2

= 2x2 â€“ x + 9 â€¦ [equation 1]

Then, we have to find out the sum of 3x2 â€“ 5x and â€“ x2 + 2x + 5

= 3x2 â€“ 5x + (-x2 + 2x + 5)

= 3x2 â€“ 5x â€“ x2 + 2x + 5

= 3x2 â€“ x2 â€“ 5x + 2x + 5

= 2x2 â€“ 3x + 5 â€¦ [equation 2]

Now, we have to subtract equation (2) from equation (1)

= 2x2 â€“ x + 9 â€“ (2x2 â€“ 3x + 5)

= 2x2 â€“ x + 9 â€“ 2x2Â + 3x â€“ 5

= 2x2 â€“ 2x2 â€“ x + 3x + 9 â€“ 5

= 2x + 4

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