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Factorise :

8(3x2y)26x+4y18(3x - 2y)^2 - 6x + 4y - 1

Factorisation

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Answer

8(3x2y)26x+4y1=8(3x2y)22(3x2y)18(3x - 2y)^2 - 6x + 4y - 1\\[1em] = 8(3x - 2y)^2 - 2(3x - 2y) - 1

Let t = (3x - 2y).

=8t22t1=8t24t+2t1=4t(2t1)+1(2t1)=(2t1)(4t+1)=(2(3x2y)1)(4(3x2y)+1)=(6x4y1)(12x8y+1)= 8t^2 - 2t - 1\\[1em] = 8t^2 - 4t + 2t - 1\\[1em] = 4t(2t - 1) + 1(2t - 1)\\[1em] = (2t - 1)(4t + 1)\\[1em] = (2(3x - 2y) - 1)(4(3x - 2y) + 1)\\[1em] = (6x - 4y - 1)(12x - 8y + 1)

Hence, 8(3x2y)26x+4y1=(6x4y1)(12x8y+1)8(3x - 2y)^2 - 6x + 4y - 1 = (6x - 4y - 1)(12x - 8y + 1).

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