Question

$factorise \: (x ^{2} - 4x)(x ^{2} - 4x - 1) - 20$
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Answer 1

Hey Pretty Stranger!

★ (x² - 4x) (x² - 4x - 1) - 20

→ (x² - 4x)² - (x² - 4x) - 20

→ y² - y - 20,where y = x² - 4x

→ y² - 5y + 4y - 20

→ y(y - 5) + 4(y - 5)

→ (y + 4) (y - 5)

→ (x² - 4x - 5) (x² - 4x + 4)

→ (x² - 5x + x - 5)(x² - 2 × x × 2 + 2²)

→ {x(x - 5) + x(x - 5)} (x - 2)²

$\large\boxed{ \purple{ \sf \: (x - 5)(x + 1)( x - 2) ^{2} }}$

In the 6th line, I've replaced y by x² - 4x.

PS - That number is replaceable, Do not replace people in your life, It.. it.. it hurts ._. xD