Expand
(i) (2x + 5y)3
(ii) (5p – 3q)3
(iii) (-a + 2b)3
(i) Using the identity
(x + y)3 = x3 + 3x2y + 3xy2 + y3 we get
(2x + 5y)3 = (2x)3 + 3(2x)2 (5y) + 3(2x)(5y)2 + (5y)3
= 8x3 + 60x2y + 150xy2 + 25y3
(ii) Using the identity
(x - y)3 = x3 - 3x2y + 3xy2 - y3 we get
(5p - 3q)3 = (5p)3-3(5p)2(3q)+3(5p)(3q)2-(3q)3
= 125p3 - 225p2q + 135pq2 - 27q3
(iii) Using the identity for (x + y)3 we get
(-a + 2b)3 = (-a)3+3(-a)2(2b)+3(-a)(2b)2+(2b)3
= a3 + 6a2b - 12ab2 + 8b3