Question

Factorise : $2x^2-24x+72$

Answer 1

Given: $2x^2-24x+72$

$=2(x^2-12x+36)$, (take 2 common)

$=2(x^2-6x-6x+36)$, (split middle term)

$=2\left[\right(x^2-6x)+(-6x+36\left)\right]$,( group pair of terms)

$=2\left[x\right(x-6)-6(x-6\left)\right]$, (factor each binomials)

$=2(x-6)(x-6)$

$=2(x-6{)}^2$

Aliter, use $(a-b{)}^2=a^2-2ab+b^2$

$\Rightarrow 2(x^2-12x+36)=2(x^2-2\times 6x+6^2)=2(x-6{)}^2$