Question
Factorize:
x3 + 8y3 + 6x2y + 12xy2
x3 + 8y3 + 6x2y + 12xy2
✓
Answer
x3 + 8y3 + 6x2y + 12xy2
= (x)3 + (2y)3 + 3 × x2 × 2y + 3 × x × (2y)2
= (x + 2y)3 $\big[\because$ a3 + b3 + 3a2b + 3ab2 = (a + b)3$\big]$
= (x + 2y)(x + 2y)(x + 2y)
$\therefore$ x3 + 8y3 + 6x2y + 12xy2
= (x + 2y)(x + 2y)(x + 2y)
= (x)3 + (2y)3 + 3 × x2 × 2y + 3 × x × (2y)2
= (x + 2y)3 $\big[\because$ a3 + b3 + 3a2b + 3ab2 = (a + b)3$\big]$
= (x + 2y)(x + 2y)(x + 2y)
$\therefore$ x3 + 8y3 + 6x2y + 12xy2
= (x + 2y)(x + 2y)(x + 2y)
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