b) (a + b)3 – (a – b)3
=[(a + b) – (a – b)][(a + b)2 + (a + b)(a – b) + (a – b)2]
= (a + b – a + b)(a2 + 2ab + b2 + a2 – b2 + a2 – 2ab + b2)
= 2a(3a2 + b2)
c) (a + b)3 + (a – b)3
= [(a + b) + (a – b)][(a + b)2 – (a + b)(a – b) + (a – b)2]
= (a + b + a – b)(a2 + 2ab + b2 – a2 + b2 + a2 – 2ab + b2]
= 2a(a2 + 3b2)
d) 8x3 + 12x2y + 6xy2 + y3
= (2x)3 + 3(2x)2(y) + 3(2x)(y)2 + (y)3
= (2x + y)3
e) – x3 + 9x2 – 27x + 27
= 27 – 27x + 9x2 – x3
= (3)3 – 3(3)2(x) + 3(3)(x)2 – (x)3
= (3 – x)3
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