Question

factorise $a^{2} - 8 b^{3} - 64 c^{3} - 24 abc$

Answer 1

The question should be:
Factorise: $a^{3} - 8b^{3} - 64c^{3} -24abc$
⇒$(a)^{3} + (-2b)^{3} + (-4c)^{3} - 24abc$
⇒$(a - 2b - 4c) (a^{2} + 4b^{2} + 16c^{2} + 2ab - 8bc +4ac)$
Used identity : x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx)