Question

Factorize (a - 2b) cube - 512b cube

Answer 1

Solution :-

• Factorise
• $\sf \: ( {a - 2b)}^{3} - 512 {b}^{3}$

$\sf \: ( {a - 2b)}^{3} - 512 {b}^{3} \\ \\ = \sf \: ( {a - 2b)}^{3} - {(8b)}^{3}$

$= \sf \: (a - 2b - 8b) \{ (a - 2b)^{2} + (a - 2b)(8b) + ( {8b)}^{2} \}\\ \\ = \sf \: (a - 10b) \{ {a}^{2} - 4ab + {4b}^{2} + 8ab - {16b}^{2} + 64 {b}^{2} \} \\ \\ \sf \: = (a - 10b) \{ {a}^{2} + 4ab + 58{b}^{2} \}$