Question
Factorize the following expressions:
(a - 2b)3 - 512b3
(a - 2b)3 - 512b3
✓
Answer
(a - 2b)3 - 512b3
= (a - 2b)3 - (8b)3
= (a - 2b - 8b)((a - 2b)2 + (a - 2b)8b + (8b)2)
$\therefore$ [a3 - b3 = (a - b)(a2 + ab + b2)]
= (a - 10b)(a2 + 4b2 - 4ab + 8ab - 16b2 + 64b2)
= (a - 10b)(a2 + 52b2 + 4ab)
$\therefore$ (a - 2b)3 − 512b3 = (a - 10b)(a2 + 52b2 + 4ab)
= (a - 2b)3 - (8b)3
= (a - 2b - 8b)((a - 2b)2 + (a - 2b)8b + (8b)2)
$\therefore$ [a3 - b3 = (a - b)(a2 + ab + b2)]
= (a - 10b)(a2 + 4b2 - 4ab + 8ab - 16b2 + 64b2)
= (a - 10b)(a2 + 52b2 + 4ab)
$\therefore$ (a - 2b)3 − 512b3 = (a - 10b)(a2 + 52b2 + 4ab)
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