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