NCERT Solutions Class 8th Maths Chapter – 8 Algebraic Expressions and Identities Exercise 8.1

(i) ab – bc, bc – ca, ca – ab

Solution:
(i) (ab – bc) + (bc – ca) + (ca – ab)
= ab – bc + bc – ca + ca – ab
= ab – ab – bc + bc – ca + ca
= 0

(ii) a – b + ab, b – c + bc, c – a + ac

Solution:
(ii) (a – b + ab) + (b – c + bc) + (c – a + ac)
= a – b + ab + b – c + bc + c – a + ac
= a – a + b – b + c – c + ab + bc + ca
= 0 + 0 + 0 + ab + bc + ca
= ab + bc + ca

(iii) 2p²q² – 3pq + 4, 5 + 7pq – 3p²q²

Solution:
(iii) 2p²q² – 3pq + 4, 5 + 7pq – 3p²q²
= (2p²q² – 3pq + 4) + (5 + 7pq – 3p²q²)
= 2p²q² – 3p²q² – 3pq + 7pq + 4 + 5
= – p²q² + 4pq + 9

(iv) l² + m² , m² + n² , n² +  l² , 2lm + 2mn + 2nl

Solution:
(iv) (l² + m²) + (m² + n²) + (n² + l²) + (2lm + 2mn + 2nl)
= l² + l² + m² + m² + n² + n² + 2lm + 2mn + 2nl
= 2l² + 2m² + 2n² + 2lm + 2mn + 2nl

Solution:
(a) (12a – 9ab + 5b – 3) – (4a – 7ab + 3b + 12)
= 12a – 9ab + 5b – 3 – 4a + 7ab – 3b – 12
= 12a – 4a – 9ab + 7ab + 5b – 3b – 3 – 12 
= 8a – 2ab + 2b – 15

(b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz

Solution:
(b) (5xy – 2yz – 2zx + 10xyz) – (3xy + 5yz – 7zx)
= 5xy – 2yz – 2zx + 10xyz – 3xy – 5yz + 7zx
= 5xy – 3xy – 2yz – 5yz – 2zx + 7zx + 10xyz
= 2xy – 7yz + 5zx + 10xyz

(c) Subtract 4p²q – 3pq + 5pq² – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq² + 5p²q

Solution:
(c) (18 – 3p – 11q + 5pq – 2pq² + 5p²q) – (4p²q – 3pq + 5pq² – 8p + 7q – 10)
= 18 – 3p – 11q + 5pq – 2pq² + 5p²q – 4p²q + 3pq – 5pq² + 8p – 7q + 10
= 18 + 10 – 3p + 8p -11q – 7q + 5pq + 3pq – 2pq² – 5pq² + 5p²q – 4p²q
= 28 + 5p – 18q + 8pq – 7pq² + p²q