Question

Factorize :(x²-4x) (x²-4x-1)-20

Answer 1

Steps :
1) Let
${x}^{2} - 4x = t$
then,
$t(t - 1) - 20 \\ = > {t}^{2} - t - 20 \\ = > {t}^{2} - 5t + 4t - 20 \\ = > t(t - 5) + 4(t - 5) \\ = > (t - 5)(t + 4)$



2) Substitute
$t = {x}^{2} - 4x$
$( {x}^{2} - 4x - 5)( {x}^{2} - 4x + 4) \\ = > (x - 5)(x + 4)( {x - 2})^{2}$