Question

Factorise each of the following: 64 $a^3$ – 27 $b^3$– 144 $a^2$b + 108a $b^2$

Answer 1

64$a^3$ – 27$b^3$ – 144$a^2$b + 108a$b^2$

= ${\left(4a\right)}^3$- ${\left(3b\right)}^3$ –3${\left(4a\right)}^2$(3b) + 3(4a)${\left(3b\right)}^2$

= ${(4a-3b)}^3$ [${(x-y)}^3$ = $x^3$ - 3$x^2$​y + 3x$y^2$​- $y^3$​]