Factorise :
(2x−y)2−14x+7y−18(2x - y)^2 - 14x + 7y - 18(2x−y)2−14x+7y−18
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(2x−y)2−14x+7y−18=(2x−y)2−7(2x−y)−18(2x - y)^2 - 14x + 7y - 18\\[1em] = (2x - y)^2 - 7(2x - y) - 18(2x−y)2−14x+7y−18=(2x−y)2−7(2x−y)−18
Let t = (2x - y).
=t2−7t−18=t2−9t+2t−18=(t2−9t)+(2t−18)=t(t−9)+2(t−9)=(t−9)(t+2)=((2x−y)−9)((2x−y)+2)=(2x−y−9)(2x−y+2)= t^2 - 7t - 18\\[1em] = t^2 - 9t + 2t - 18\\[1em] = (t^2 - 9t) + (2t - 18)\\[1em] = t(t - 9) + 2(t - 9)\\[1em] = (t - 9)(t + 2)\\[1em] = ((2x - y) - 9)((2x - y) + 2)\\[1em] = (2x - y - 9)(2x - y + 2)=t2−7t−18=t2−9t+2t−18=(t2−9t)+(2t−18)=t(t−9)+2(t−9)=(t−9)(t+2)=((2x−y)−9)((2x−y)+2)=(2x−y−9)(2x−y+2)
Hence, (2x−y)2−14x+7y−18=(2x−y−9)(2x−y+2)(2x - y)^2 - 14x + 7y - 18 = (2x - y - 9)(2x - y + 2)(2x−y)2−14x+7y−18=(2x−y−9)(2x−y+2).
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