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Factorize : (x^2-4x)(x^2-4x-1)-20...

Factorize : `(x^2-4x)(x^2-4x-1)-20`

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`(x^2-4x)(x^2-4x-1)-20`
`= (x^2 - 4x)[(x^2 - 4x) - 1] - 20`
`= (x^2 - 4x)^2 - (x^2 - 4x) - 20`
`= y^2 - y - 20 , `where` y = x^2 - 4x`
`= y^2 + 4y - 5y - 20`
`= y(y+4) - 5(y+4)`
`= (y+4)(y-5)`
`= (x^2 - 4x + 4)(x^2 - 4x - 5) [`Replacing `y` by `x^2–4x]`
`= {x^2 - 2x - 2x + 4}{x^2 + x - 5x - 5}`
`= {x(x-2) - 2(x-2)} {x(x+1) - 5(x+1)}`
`= {(x-2)(x-2)} {(x+1)(x-5)}`
`= (x+1)(x-2)(x-2)(x-5)`
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