Question
Factorize:
8x3 + 27y3 + 36x2y + 54xy2
8x3 + 27y3 + 36x2y + 54xy2
✓
Answer
8x3 + 27y3 + 36x2y + 54xy2
= (2x)3 + (3y)3 + 3 × (2x)2 × 3y + 3 × (2x)(3y)2
= (2x + 3y)3 $\big[\because$ a3 + b3 + 3a2b + 3ab2 = (a + b)3$\big]$
= (2x + 3y)(2x + 3y)(2x + 3y)
$\therefore$ 8x3 + 27y3 + 36x2y + 54xy2
= (2x + 3y)(2x + 3y)(2x + 3y)
= (2x)3 + (3y)3 + 3 × (2x)2 × 3y + 3 × (2x)(3y)2
= (2x + 3y)3 $\big[\because$ a3 + b3 + 3a2b + 3ab2 = (a + b)3$\big]$
= (2x + 3y)(2x + 3y)(2x + 3y)
$\therefore$ 8x3 + 27y3 + 36x2y + 54xy2
= (2x + 3y)(2x + 3y)(2x + 3y)
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