Question

a^3-8b^3-64a^3-24abc
Factorise the given

Answer 1

Here the given expression can be written as

$(a^{3} - 8b^{3} - 64a^{3} - 24abc = (a)^{3} + (-2b)^{3} + (-4c)^{3} - 3(a)(-2b)(-4c)$

Comparing with the given identity,

x³+ y³ + z³ - 3xyz = (x+y+z)(x²+y²+z²- xy - yz -zx)

we get the answer as

(a - 2b - 4c)(a² + (-2b)² + (-4c)² - (-2ab) - (8bc) - (-4ac))

(a - 2b - 4c)(a²+ 4b²+ 16c²+ 2ab - 8bc + 4ac)