CBSE students can refer to NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.2 Textbook Questions and Answers are provided by experts in order to help students secure good marks in exams.

## Class 7 Maths NCERT Solutions Chapter 12 Algebraic Expressions Ex 12.2

Question 1.

Simplify combining like terms:

(i) 21b – 32 + 7b – 20b

Solution:

21b – 32 + 7b – 20b

= 21b + 7b – 20b – 32

= (21 + 7 – 20 )b – 32 = 8b – 32

(ii) – z^{2} + 13 z^{2} -5z + 7z^{3} – 15z

Solution:

– z^{2} + 13 z^{2} – 5 z +7z^{3} – 15z

= 7z^{3} – z^{2} + 13z^{2} – 5z – 15z

= 7z^{3} + (-1 + 13)z^{2} + (- 5 – 15)z

= 7z^{3} +12z^{2} – 20z

(iii) P – (p – q) – q – (q – p)

Solution:

p – (p – q) – q – (q – p)

= p – p + q – q – q + p

= (p – p + p) + (q – q – q) = p – q

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

Solution:

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

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

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

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

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

(v) 5x^{2} y – 5x^{2} + 3yx^{2} – 3y^{2}+ x^{2} – y^{2} + 8xy^{2} – 3y^{2}

Solution:

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

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

(vi) (3y^{2} + 5y – 4) – (8y – y^{2} – 4)

Solution:

(3y^{2} + 5y – 4) – (8y – y^{2} – 4)

= 3y^{2} + 5y – 4 – 8y – y^{2} + 4

= 3y^{2} + y^{2} + 5y – 8y – 4 + 4

= (3 + 1)y^{2} + (5 – 8)y + (- 4 + 4)

= 4y^{2} – 3y

Question 2.

Add:

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

Solution:

Required sum:

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

= (3 – 5 + 8 – 4) mn

= (11 – 9) mn

= 2 mn

(ii) t – 8tz, 3tz – z, z – t

Solution:

Required sum:

= (t – 8tz) + (3tz – z) + (z – t)

= t – 8tz + 3tz – z + z – t

= t – t – 8tz + 3tz – z + z

= (1 – 1) t + (-8 + 3)tz + (-1 + 1)z

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

= 0 – 5tz + 0

= -57z

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

Solution:

Required sum:

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

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

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

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

= 12mn – 4

(iv) a + 6 – 3 ,6 – a + 3, a – 6 + 3

Solution:

Required sum:

= (a + b – 3) + (b – a + 3) + (a – b + 3)

= a + b – 3 + b – a + 3 + a – b + 3

= (a – a + a) + (b + b – b) + (- 3 + 3 + 3)

= (1 – 1 – 1)a + (1 + 1 – 1) b + 3

= a + b + 3

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

Solution:

Required sum:

= (14x + 10y – 12xy – 13) + (18 – 7x – 10y + 8xy) + 4xy

= 14x + 10y – 12xy – 13 + 18 – 7x -10y + 8xy + 4xy

= 14x – 7x + 10y – 10y – 12xy + 8xy + 4xy – 13 + 18

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

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

= 7x + 5

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

Solution:

Required sum:

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

= 5m – 7n +3n – 4m + 2 + 2m – 3mn – 5

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

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

= 3m – 4n – 3mn – 3

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

Solution:

Required sum:

= 4x^{2 }y (-3xy^{2}) + (- 5xy^{2}) + 5x^{2 }y

= 4x^{2 }y – 3xy^{2} – 5xy^{2 }+ 5x^{2 }y

= 4x^{2 }y + 5x^{2 }y – 3xy^{2} – 5xy^{2}

= (4 +5)x^{2}y + (- 3 – 5)xy^{2}

= 9x^{2} y – 8xy^{2}

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

Solution:

Required sum:

= (3p^{2}q^{2} – 4pq +5)+ (- 10p^{2}q^{2}) + (15 +9 pq +7p^{2}q^{2})

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

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

= (3 – 10 + 7)p^{2}q^{2} + (- 4 + 9) pq + (5 +15)

= (0)p^{2}q^{2 }+ 5pq + 20

= 0 + 5pq + 20 = 5pq + 20

(ix) ab – 4a, 4b – ab, 4a – 4b

Solution:

Required sum:

=(ab – 4a) + (4b – ab) + (4a – 4b)

= ab – 4a + 4b – ab + 4a – 4b

= ab – ab – 4a + 4a + 4b – 4b

= (1 – 1)ab + (- 4 + 4)a + (4 – 4)b

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

(x) x^{2} – y^{2} – 1, y^{2} – 1 – x^{2},1 – x^{2} – y^{2}

Solution:

Required sum:

= (x^{2} – y^{2} – 1) + (y^{2} -1 – x^{2}) + (1 – x^{2} – y^{2})

= 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

= (1 – 1 – 1)x^{2} + (- 1 + 1 – 1)y^{2} +(-1-1+1)

= x^{2} – y^{2} – 1

Question 3.

Subtract:

(i) – 5y^{2} from y^{2}

Solution:

The required difference is given by

y^{2} – (- 5y^{2}) = y^{2} + 5y^{2} = (1 + 5)y^{2} = 6y^{2}

(ii) 6xy from – 12xy

Solution:

The required difference is given by

(- 12xy) – 6xy = (-12 – 6)xy

= – 18xy

(iii) (a – b) from (a + b)

Answer:

The required difference is given by

(a + b) – (a – b) = a + b- a + b

= a – a + b + b

= (1 – 1 )a + (1 + 1)b = 2b

(iv) a (b – 5) from b (5 – a)

Solution:

The required difference is given by

b (5 – a) – a (b – 5) = 5b – ab – ab + 5a

= 5a + 5b + (-1 – 1)ab

= 5a + 5b – 2 ab

(v) – m^{2} 5mn from 4m^{2 }– 3mn + 8

Solution:

The required difference is given by

(4m^{2} – 3mn + 8) – (-m^{2} + 5mn)

= 4m^{2} – 3mn + 8 + m^{2} – 5mn

= 4m^{2} + m^{2} – 3mn – 5mn + 8

= (4 + 1)m^{2} + (- 3 – 5)mn + 8

= 5m^{2} – 8 mn + 8

(vi) – x^{2} + 10x – 5 from 5x – 10

Solution:

The required difference is given by

(5x -10) – (- x^{2} + 10x – 5)

= 5x -10 + x^{2} -10x + 5

= x^{2} + (5 – 10)x + (- 10 + 5)

= x^{2} – 5x – 5

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

Solution:

The required difference is given by

(3ab – 2a^{2} – 2b^{2}) – (5a^{2} – 7ab + 5b^{2})

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

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

= (- 2 – 5)a^{2} + ( -2 – 5)b^{2} + (3 + 7)ab

= -7a^{2} – 7b^{2} +10ab

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

Solution:

The required difference is given by

(5p^{2}+3q^{2} – pq) – (4pq – 5q^{2} – 3p^{2})

= 5p^{2} + 3q^{2} – pq – 4pq , 5q^{2} + 3p^{2}

= 5p^{2} + 3q^{2} + 5q^{2} – pq – 4pq

= (5 + 3)p^{2} + (3 + 5)q^{2} +(- 1 – 1 – 4)pq

= 8p^{2} + 8q^{2} – 5pq

Question 4.

(a) What should be added to x^{2} + xy + y^{2} to obtain 2x 2 + 3xy?

Solution:

Required expression is equal to the subtraction of x^{2} + xy + y^{2} from 2x^{2} + 3xy.

Hence, required 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}

= (2 – 1)x^{2} + (3-1 ) xy – y^{2}

= x^{2} + 2xy – y^{2}

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

Solution:

Let P denote the required expression, then (2a + 8b +10) – P = – 3a + 7b +16

Hence, required expression P

= (2a + 8b + 10) – (-3a + 7b + 16)

= 2a + 8b +10 + 3a – 7b -16

= 2a + 3a + 8b-7b+ 10 – 16

= (2 + 3)a + (8 – 7)b + (10 -16)

= 5a + b – 6

Question 5.

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

Solution:

Let P denote the required expression, then

(3x^{2} – 4y^{2} + 5xy + 20) – P = (- x^{2} – y^{2} + 6xy + 20)

Hence, required expression P

= (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} + 5xyy – 6xy + 20 – 20

= (3 +1)x^{2} + (- 4 +1)y2 +(5 -6)xy + (20 – 20)

= 4x^{2} – 3y^{2} – xy

Question 6.

(a) From the sum of 3x – y +11 and -y -11, subtract 3 x – y – 11.

Solution:

The sum of 3x – y +11 and -y -11 is given by

(3x – y + 11) + (- y – 11) = 3x – y + 11 -y – 11 = 3x – 2y

Now, we have to subtract 3x – y -11 from 3x – 2y

∴ Required expression = (3x – 2y) – (3x – y -11)

= 3x – 2y- 3x + y + 11 = -y + 11

(b) From the sum of 4 + 3x and 5 – 4x + 2x^{2}, subtract the sum of 3x^{2} – 5x and – x^{2} + 2x + 5.

Solution:

The sum of 4 + 3x and 5 – 4x + 2x^{2} is given by

(4 + 3x) + (5 – 4x + 2x^{2}) = 4 + 3x + 5 – 4x + 2x^{2}

= 9 – x + 2x^{2}

The sum of 3xThe sum of 4 + 3x and 5 – 4x + 2x^{2} is given by

(4 + 3x) + (5 – 4x + 2x^{2}) = 4 + 3x + 5 – 4x + 2x^{2}

= 9 – x + 2x^{2} – 5x and – x^{2} + 2x + 5 is given by

(3x^{2} – 5x) + (-x^{2} + 2x + 5)

= 2x^{2} – 3x + 5

Now, we have to subtract 2x^{2} – 3x + 5 from 9 – x + 2x^{2}

∴ Required expression = (9 – x + 2x^{2}) – (2x^{2} – 3x + 5)

= 9 – x + 2x^{2} – 2x^{2} + 3x – 5

= 2x + 4