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Mathematics

Factorise :

(2xy)214x+7y18(2x - y)^2 - 14x + 7y - 18

Factorisation

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Answer

(2xy)214x+7y18=(2xy)27(2xy)18(2x - y)^2 - 14x + 7y - 18\\[1em] = (2x - y)^2 - 7(2x - y) - 18

Let t = (2x - y).

=t27t18=t29t+2t18=(t29t)+(2t18)=t(t9)+2(t9)=(t9)(t+2)=((2xy)9)((2xy)+2)=(2xy9)(2xy+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)

Hence, (2xy)214x+7y18=(2xy9)(2xy+2)(2x - y)^2 - 14x + 7y - 18 = (2x - y - 9)(2x - y + 2).

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