Question

factorise : (x^2-4x) (x^2- 4x+1) - 20

Answer 1

Let's simplify step-by-step.
(x2−4x)(x2−4x+1)−20

Distribute:

=(x2)(x2)+(x2)(−4x)+(x2)(1)+(−4x)(x2)+(−4x)(−4x)+(−4x)(1)+−20

=x4+−4x3+x2+−4x3+16x2+−4x+−20

Combine Like Terms:

=x4+−4x3+x2+−4x3+16x2+−4x+−20

=(x4)+(−4x3+−4x3)+(x2+16x2)+(−4x)+(−20)

=x4+−8x3+17x2+−4x+−20

Answer:

=x4−8x3+17x2−4x−20.

Answer 2

$\huge{\dag\sf\purple{ANSWER}}$

$(x {}^{2} - 4x)(x {}^{2} - 4x + 1) - 20 \\ \\ a(a + 1) - 20 \\ \\ a {}^{2} + a - 20$

$\begin{gathered}\mapsto\sf\boxed{\bold{\pink{Splitting \: the \: middle \: term}}}\\\end{gathered}$

$(a + 5)(a - 4)$

$(x {}^{2} - 4x + 5)(x {}^{2} - 4x - 4)$

$\huge{\sf\red{@ItzIshu}}$