NCERT Solutions Class 7 Mathematics Algebraic Expressions Ex 12.2

Question : 1.Simplify combining like terms:

1. 21b – 32 + 7b – 20b
2. – z² + 13z² – 5z + 7z³ – 15z
3. p – (p – q) – q – (q – p)
4. 3a – 2b – ab – (a – b + ab) + 3ab + b – a
5. 5𝓍²y – 5𝓍² + 3y𝓍² – 3y² + 𝓍² – y² + 8𝓍y² – 3y²
6. (3y² + 5y – 4) – (8y – y² – 4)

Answer :
(i) 21b – 32 + 7b – 20b = 21b + 7b – 20b – 32

= 28b – 20b – 32 = 8b – 32

(ii) – z² + 13z² – 5z + 7z³ – 15z = 7z³ + ( – z² + 13z²) – (5z + 15z)

= 7z³ + 12z² – 20z

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

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

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

= a – 0 – ( – ab)

= a + ab

(v) 5𝓍²y – 5𝓍² + 3y𝓍² – 3y² + 𝓍² – y² + 8𝓍y² – 3y²

= 5𝓍²y + 3y𝓍² + 8𝓍y² – 5𝓍² + 𝓍² – 3y² – y² – 3y²

= (5𝓍²y + 3𝓍²y) + 8𝓍y² – (5𝓍² – 𝓍²) – (3y² + y² + 3y²)

= 8𝓍²y + 8𝓍y² – 4𝓍² – 7y²

(vi) (3y² + 5y – 4) – (8y – y² – 4) = 3y² + 5y – 4 – 8y + y² + 4

= (3y² + y²) + (5y – 8y) – (4 – 4)

= 4y² – 3y – 0 = 4y² – 3y

Question : 2.Add:

1. 3mn, – 5mn, 8mn – 4mn
2. t – 8tz, 3tz – z, z – t
3. – 7mn + 5, 12mn + 2, 9mn – 8, – 2mn – 3
4. a + b – 3,b – a + 3,a – b + 3
5. 14𝓍 + 10y – 12𝓍y – 13, 18 – 7𝓍 – 10y + 8𝓍y, 4𝓍y
6. 5m – 7n, 3n – 4m + 2, 2m – 3mn – 5
7. 4𝓍²y, – 3𝓍y², – 5𝓍y², 5𝓍²y
8. 3p²q² – 4pq + 5, – 10p²q², 15 + 9pq + 7p²q²
9. ab – 4a, 4b – ab, 4a – 4b
10. 𝓍² – y² – 1, y² – 1 – 𝓍², 1 – 𝓍² – y²

Answer :
(i)
3mn, – 5mn,8mn, – 4mn = 3mn + ( – 5mn) + 8mn + ( – 4mn)

= (3 – 5 + 8 – 4)mn = 2mn

(ii)
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 – 5tz + 0 = – 5tz

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

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

= ( – 7 + 12 + 9 – 2)mn + 7 – 11

= 12mn – 4

(iv)
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

= a + b + 3

(v)
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

= 7𝓍 + 0y + 0𝓍y + 5 = 7𝓍 + 5

(vi)
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 – 3

= 3m – 4n + 3mn – 3

(vii)
4𝓍²y, – 3𝓍y², – 5𝓍y²,5𝓍²y = 4𝓍²y + ( – 3𝓍y²) + ( – 5𝓍y²) + 5𝓍²y

= 4𝓍²y + 5𝓍²y – 3𝓍y² – 5𝓍y²

= 9𝓍²y – 8𝓍y²

(viii)
3p²q² – 4pq + 5, – 10p²q²,15 + 9pq + 7p²q²

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

= 3p²q² – 10p²q² + 7p²q² + 4pq + 9pq + 5 + 15

= (3 – 10 + 7)p²q² + ( – 4 + 9)pq + 20

= 0p²q² + 5pq + 20 = 5pq + 20

(ix)
ab – 4a,4b – ab,4a – ab = ab – 4a + 4b – ab + 4a – ab

= – 4a + 4a + 4b – 4b + ab – ab

= 0 + 0 + 0 = 0

(x)
𝓍² – y² – 1,y² – 1 – 𝓍²,1 – 𝓍² – y² = 𝓍² – y² – 1 + y² – 1 – 𝓍² + 1 – 𝓍² – y²

= 𝓍² – 𝓍² – 𝓍² – y² + y² – y² – 1 – 1 + 1

= (1 – 1 – 1)𝓍² + ( – 1 + 1 – 1)y² – 1 – 1 + 1

= – 𝓍² – y² – 1

Question : 3.Subtract:

1. – 5y² fromy²
   
   
2. 6𝓍y from – 12𝓍y
   
   
3. (a – b) from (a + b)
   
   
4. a(b – 5) from b(5 – a)
   
   
5. – m² + 5mn from 4m² – 3mn + 8
   
   
6. – 𝓍² + 10𝓍 – 5 from 5𝓍 – 10
   
   
7. 5a² – 7ab + 5b² from ab – 2a² – 2b²
   
   
8. 4pq – 5q² – 3p² from 5p² + 3q² – pq
   
   

Answer :
(i) y² – ( – 5y²) = y² + 5y² = 6y²

(ii) – 12𝓍y – (6𝓍y) = – 12𝓍y – 6𝓍y = – 18𝓍y

(iii) (a + b) – (a – b) = a + b – a + b = a – a + b + b = 2b

(iv) b(5 – a) – a(b – 5) = 5b – ab – ab + 5a = 5b – 2ab + 5a = 5a + 5b – 2ab

(v) 4m² – 3mn + 8 – ( – m² + 5mn) = 4m² – 3mn + 8 + m² – 5mn

= 4m² + m² – 3mn – 5mn + 8

= 5m² – 8mn + 8

(vi) 5𝓍 – 10 – ( – 𝓍² + 10𝓍 – 5) = 5𝓍 – 10 + 𝓍² – 10𝓍 + 5

= 𝓍² + 5𝓍 – 10𝓍 – 10 + 5 = 𝓍² – 5𝓍 – 5

(vii) 3ab – 2a² – 2b² – (5a² – 7ab + 5b²) = 3ab – 2a² – 2b² – 5a² + 7ab – 5b²

= 3ab + 7ab – 2a² – 5a² – 2b² – 5b²

= 10ab – 7a² – 7b²

= – 7a² – 7b² + 10ab

(viii) 5p² + 3q² – pq – (4pq – 5q² – 3p²) = 5p² + 3q² – pq – 4pq + 5q² + 3p²

= 5p² + 3p² + 3q² + 5q² – pq – 4pq

= 8p² + 8q² – 5pq