Factorise: $(x^{2} + 4 x) (x^{2} 4 x - 1) - 20$

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Solution

$(x^{2} - 4 x) (x^{2} - 4 x - 1) - 20$
let $(x ² - 4 x) = P$

$P (P - 1) - 20$
$P ² - P - 20$
$P ² - 5 P + 4 P - 20$
$P (P - 5) + 4 (P - 5)$
$(P + 4) (P - 5)$
put $P = x^{2} - 4 x$

$(x ² - 4 x + 4) (x ² - 4 x - 5)$
$(x - 2)^{2} (x + 1) (x - 5)$

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