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

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Solution

given, $(x^{2} - 4 x) (x^{2} - 4 x - 1) - 20$

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

$= y^{2} - y - 20$ , where $y = x^{2} - 4 x$

$= y^{2} - 5 y + 4 y - 20$

$= y (y - 5) + 4 (y - 5)$

$= (y - 5) (y + 4)$

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

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

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

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Similar questions

y = \frac{1 + \frac{1}{x^{2}}}{1 - \frac{1}{x^{2}}}

\frac{d y}{d x} =

- \frac{4 x}{{(x^{2} - 1)}^{2}}

- \frac{4 x}{x^{2} - 1}

\frac{1 - x^{2}}{4 x}

\frac{4 x}{x^{2} - 1}

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

x^{2} + 4 x + 1

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