please help me in this question ☝
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lets suppose (x²-4x) be y
so, the equation becomes
(y)(y-1)-20 => y²-y-20
y²-y-20
=> y²-5y+4y-20. (splitting the middle term)
=> y(y-5)+4(y-5)
=> (y-5)(y+4)
substitute y = (x²-4x)
=> (y-5)(y+4)
=> (x²-4x-5)(x²-4x+4)
=> (x²-5x+x-5)(x²-2x-2x+4).
=>[x(x-5)+1(x-5)] [x(x-2)-2(x-2)]. (by splitting the middle term)
[(x-5)(x+1)] [(x-2)(x-2)]
=> (x-5)(x+1)(x-2)(x-2)
hope this helps
so, the equation becomes
(y)(y-1)-20 => y²-y-20
y²-y-20
=> y²-5y+4y-20. (splitting the middle term)
=> y(y-5)+4(y-5)
=> (y-5)(y+4)
substitute y = (x²-4x)
=> (y-5)(y+4)
=> (x²-4x-5)(x²-4x+4)
=> (x²-5x+x-5)(x²-2x-2x+4).
=>[x(x-5)+1(x-5)] [x(x-2)-2(x-2)]. (by splitting the middle term)
[(x-5)(x+1)] [(x-2)(x-2)]
=> (x-5)(x+1)(x-2)(x-2)
hope this helps
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