Q. 193.8( 8 Votes )

Factorize each of the following expressions:

x3+6x2+12x+16

Answer :

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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