Question

Factorise:
$2{(a-2b)}^2-25(a-2b)+12$

Answer 1

Let $(a-2b)=p$, then the equation $2(a-2b{)}^2-25(a-2b)+12$ becomes $2p^2-25p+12$

Consider the expression $2p^2-25p+12$ we can factorise it as follows:

$2p^2-25p+12=2p^2-24p-p+12=2p(p-12)-1(p-12)=(2p-1)(p-12)$

Now, substitute the value of $p$ as $p=(a-2b)$:

$(p-12)(2p-1)=(a-2b-12)\left(2\right(a-2b)-1)=(a-2b-12)(2a-4b-1)$

Hence, $2(a-2b{)}^2-25(a-2b)+12=(a-2b-12\left)\right(2a-4b-1)$