Class 7 Maths

# Algebraic Expressions NCERT Exercise 12.2

Question 1: Simplify combining like terms:

(a) 21b – 32 + 7b – 20b

Answer: 21b – 32 + 7b – 20b

= 21b + 7b – 20b – 32

= 28b – 20b – 32 = 8b – 32

(b) – z^2 + 13z^2 – 5z + 7z^3 – 15z

Answer: - z^2 + 13z^2 – 5z + 7z^3 – 15z

= - z^2 + 13z^2 – 5z – 15z + 7z^3

= 12z^2 – 20z + 7z^3

(c) p – (p – q) – q – (q – p)

Answer: p – (p – q) – q – (q – p)

= p – p + q – q – q + p

= p – p + p + q – q – q

= p – q

(d) 3a – 2b – ab – (a – b + ab) + 3ab + b – a

Answer: 3a – 2b – ab – a + b – ab + 3ab + b – a

= 3a – a – a – 2b + b + b – ab – ab + 3ab

= 3a – 2a – 2b + 2b – 2ab + 3ab

= a + ab

(e) 5x^2y – 5x^2 + 3yx^2 – 3y^2 + x^2 – y^2 + 8xy^2 – 3y^2

Answer: 5x^2y – 5x^2 + 3yx^2 – 3y^2 + x^2 – y^2 + 8xy^2 – 3y^2

= 5x^2y + 3x^2y – 5x^2 + x^2 – 3y^2 – y^2 + 8xy^2

= 8x^2y – 4x^2 – 4y^2 + 8xy^2

(f) (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

= 3y^2 + y^2 + 5y – 8y – 4 + 4

= 4y^2 – 3y

(a) 3mn, - 5mn, 8mn, - 4mn

Answer: 3mn – 5mn + 8mn – 4mn

= 3mn + 8mn – 5mn – 4mn

= 11mn – 9mn = 8mn

(b) t – 8tz, 3tz – z, z – t

Answer: t – 8tz + 3tz – z + z – t

= t – t – 8tz + 3tz – z + z

= - 5tz

(c) – 7mn + 5, 12mn + 2, 9mn – 8, - 2mn – 3

Answer: – 7mn + 5 + 12mn + 2 + 9mn – 8 - 2mn – 3

= - 7mn + 12mn + 9mn – 2mn + 5 + 2 – 8 – 3

= 12mn + 7 – 11

= 12mn – 4

(d) a + b – 3, b – a + 3, a – b + 3

Answer: a + b – 3 + b – a + 3 + a – b + 3

= a – a + a + b + b – b – 3 + 3 + 3

= a + b + 3

(e) 14x + 10y – 12xy – 13, 18 – 7x – 19y + 8xy, 4xy

Answer: 14x + 10y – 12xy – 13 + 18 – 7x – 19y + 8xy + 4xy

= 14x – 7x – 10y – 19y – 12xy + 7xy + 4xy – 13 + 18

= 7x – 29y – xy + 5

(f) 5m – 7n, 3n – 4m + 2, 2m - 3mn – 5

Answer: 5m – 7n + 3n – 4m + 2 + 2m - 3mn – 5

= 5m – 4m + 2m – 7n + 3n – 3mn + 2 – 5

= 3m – 4n – 3mn – 3

(g) 4x^2y, - 3xy^2, - 5xy^2, 5x^2y

Answer: 4x^2y - 3xy^2 - 5xy^2 + 5x^2y

= 4x^2y + 5x^2y – 3xy^2 – 5xy^2

= 9x^2y – 8xy^2

(h) 3p^2q^2 – 4pq + 5, - 10p^2q^2, 15 + 9pq + 7p^2q^2

Answer: 3p^2q^2 – 4pq + 5 - 10p^2q^2 + 15 + 9pq + 7p^2q^2

= 3p^2q^2 – 10p^2q^2 + 7p^2q^2 – 4pq + 9pq + 5 + 15

= 10p^2q^2 – 10p^2q^2 + 5pq + 20

= 5pq + 20

(i) ab – 4a, 4b – ab, 4a – 4b

Answer: ab – 4a + 4b – ab + 4a – 4b

= ab – ab – 4a + 4a + 4b – 4b = 0

(j) x^2 – y^2 – 1, y^2 – 1 – x^2, 1 – x^2 – y^2

Answer: x^2 – y^2 – 1 + y^2 – 1 – x^2 + 1 – x^2 – y^2

= x^2 – x^2 – x^2 – y^2 + y^2 – y^2 – 1 – 1 + 1

= - x^2 – y^2 – 1

Question 3: Subtract the following:

(a) 0.5y^2 from y^2

Answer: y^2 – 0.5y^2 = 0.5y^2

(b) 6xy from – 12xy

Answer: - 12xy – 6xy = - 18xy

(c) (a – b) from (a + b)

Answer: a + b – (a – b) = a + b – a + b = 2b

(d) a(b – 5) from b(5 – a)

Answer: b(5 – a) – a(b – 5)

= 5b – ab – ab + 5a = 5a + 5b – 2ab

(e) – m^2 + 5mn from 4m^2 – 3mn + 8

Answer: 4m^2 – 3mn + 8 – ( - m^2 + 5mn)

= 4m^2 – 3mn + 8 + m^2 – 5mn

= 4m^2 + m^2 – 3mn – 5mn + 8

= 5m^2 – 8mn + 8

(f) – x^2 + 10x – 5 from 5x – 10

Answer: 5x – 10 – ( - x^2 + 10x – 5)

= 5x – 10 + x^2 – 10x + 5

= 5x – 10x + x^2 – 10 + 5

= - 5x + x^2 – 5

(g) 5a^2 – 7ab + 5b^2 from 3ab – 2a^2 – 2b^2

Answer: 3ab – 2a^2 – 2b^2 – (5a^2 – 7ab + 5b^2)

= 3ab – 2a^2 – 2b^2 – 5a^2 + 7ab – 5b^2

= 3ab + 7ab – 2a^2 – 5a^2 – 2b^2 – 5b^2

= 10ab – 7a^2 – 7b^2

(h) 4pq – 5q^2 – 3p^2 from 5p^2 + 3q^2 – pq

Answer: 5p^2 + 3q^2 – pq – (4pq – 5q^2 – 3p^2)

= 5p^2 + 3q^2 – pq – 4pq + 5q^2 + 3p^2

= 5p^2 + 3p^2 + 3q^2 + 5q^2 – pq – 4pq

= 8p^2 + 8q^2 – 5pq

Question 4: What should be added to x^2 + xy + y^2 to obtain 2x^2 + 3xy?

Answer: For this, you need to subtract the first expression from the second expression:

= 2x^2 + 3xy – (x^2 + xy + y^2)

= 2x^2 + 3xy – x^2 – xy – y^2

= 2x^2 – x^2 + 3xy – xy – y^2

= x^2 + 2xy – y^2

Question 5: What should be subtracted from 2a + 8b + 10 to get – 3a + 7b + 16?

Answer: For this, you need to subtract the second expression from first expression:

= 2a + 8b + 10 – ( - 3a + 7b + 16)

= 2a + 8b + 10 + 3a – 7b – 16

= 2a + 3a + 8b – 7b + 10 – 16

= 5a + b – 6

Question 6: What should be taken away from 3x^2 – 4y^2 + 5xy + 20 to obtain – x^2 – y^2 + 6xy + 20?

Answer: For this, you need to subtract the second term from first term:

= 3x^2 – 4y^2 + 5xy + 20 – (– x^2 – y^2 + 6xy + 20)

= 3x^2 – 4y^2 + 5xy + 20 + x^2 + y^2 – 6xy – 20

= 3x^2 + x^2 – 4y^2 + y^2 + 5xy – 6xy + 20 – 20

= 4x^2 – 3y^2 – xy

Question 7: From the sum of 3x – y + 11 and – y – 11, subtract 3x – y – 11.

Answer: 3x – y + 11 + (– y – 11) – (3x – y – 11)

= 3x – y + 11 – y – 11 – 3x + y + 11

= 3x – 3x – y – y + y + 11 – 11 + 11

= - y + 11

Question 8: From the sum of 4 + 3x and 5 – 4x + 2x^2, subtract the sum of 3x^2 – 5x and – x^2 + 2x + 5.

Answer: Sum of first pair of expressions:

4 + 3x + 5 – 4x + 2x^2

= 4 + 5 + 3x – 4x + 2x^2 = 9 – x + 2x^2

Sum of second pair of expressions:

3x^2 – 5x – x^2 + 2x + 5

= 3x^2 – x^2 – 5x + 2x + 5

= 2x^2 – 3x + 5

Subtraction: 9 – x + 2x^2 – (2x^2 – 3x + 5)

= 9 – x + 2x^2 – 2x^2 + 3x – 5

= 2x^2 – 2x^2 – x + 3x + 9 – 5

= 2x + 4`