Factorise: (x^2-4x) (x^2-4x-1) -20

1.	Factorise: (x^2-4x) (x^2-4x-1) -20
Answer» Answer: $(x-5)(x+1)(x-2)^{2}$ Step-by-step explanation: $(x^{2} - 4x)(x^{2} -4x -1) - 20$ Let $x^{2} - 4x$ be = a $(a)(a -1) - 20\\$ $=a^{2} -a - 20$ Now, FACTORISE it USING middle TERM splitting. $= a^{2} -5a + 4a - 20$ $= a(a - 5) + 4(a - 5)$ $= (a-5)(a+4)$ Now, put the value of 'a'. $= (x^{2} - 4x -5)(x^{2} - 4x + 4)$ Now, factorise the TWO quadratic expressions in the brackets by middle term splitting. You will get 4 factors (2 factors of each EXPRESSION). $= [x^{2} - 5x + x -5][x^{2} - 2x -2x + 4]$ $= [x(x-5) + 1(x -5)][x(x-2)-2(x -2)]$ $= (x-5)(x+1)(x-2)(x-2)$ $= (x-5)(x+1)(x-2)^{2}$

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