Factorize each of the following expressions:
x3+6x2+12x+16
Given,
X3 +6x212x+16 = (x3 + 6x2+12x+8)+8
= (x+2)3 + 8 [∵ (a+b)3 = a3 + b3 +3ab(a+b)]
= (x+2)3 + (2)3
= (x+2+2) {(x+2)2 +4 – 2 (x+2)}
= (x+4)(x2+4+4x+4 - 2x - 4)
= (x+4)(x2+2x+4)
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