Question

factorise X3+8y3+64z3-24xyz​

Answer 1

Answer:

$\sf \: x^3−8y^3−64z^3−24xyz \\ \\\sf \: a^3+b^3+c^3−3abc \\ \\ \sf=(a+b+c) \\ \\\sf(a^2+b^2+c^2−ab−bc−ca)$

Comparing with the expression of standard formulae,

Here,

$\sf \: a=x \\ \\ \sf \: b=−2y \\ \\ \sf \: c=−4z \\ \\ \sf \: Therefore, \\ \\\sf=>x^3+(−2y)^3+(−4z)^3−3(x) \sf(−2y)(−4z) \\ \\ \sf=(x−2y−4z) \\ \\\sf(x^2+4y^2+16z^2+2xy−8yz+4xz)$