Q113Multiple choice
Verify the following:
- (i)(ab + bc) (ab – bc) + (bc + ca) (bc – ca) + (ca + ab) (ca – ab) = 0
- (ii)(a + b + c) (a2 + b2 + c 2 – ab – bc – ca) = a3 + b3+ c 3 – 3abc
- (iii)(p – q) (p2 + pq + q2) = p3 – q3
- (iv)(m + n) (m 2 – mn + n2) = m 3 + n3 (v) (a + b) (a + b) (a + b) = a3 + 3a2b + 3ab2 + b3 (vi) (a – b) (a – b) (a – b) = a3 – 3a2b + 3ab2 – b3 (vii) (a2 – b2) (a2 + b2) + (b2 – c 2) (b2 + c 2) + (c 2 – a2) + (c 2 + a2) = 0 (viii) (5x + 8)2 – 160x = (5x – 8)2 (ix) (7p – 13q)2 + 364pq = (7p + 13q)2 2 2 3p 7 3 7 (x) + − p+ =2 7 6p 7 6p