Factorise :
8(3x−2y)2−6x+4y−18(3x - 2y)^2 - 6x + 4y - 18(3x−2y)2−6x+4y−1
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8(3x−2y)2−6x+4y−1=8(3x−2y)2−2(3x−2y)−18(3x - 2y)^2 - 6x + 4y - 1\\[1em] = 8(3x - 2y)^2 - 2(3x - 2y) - 18(3x−2y)2−6x+4y−1=8(3x−2y)2−2(3x−2y)−1
Let t = (3x - 2y).
=8t2−2t−1=8t2−4t+2t−1=4t(2t−1)+1(2t−1)=(2t−1)(4t+1)=(2(3x−2y)−1)(4(3x−2y)+1)=(6x−4y−1)(12x−8y+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)=8t2−2t−1=8t2−4t+2t−1=4t(2t−1)+1(2t−1)=(2t−1)(4t+1)=(2(3x−2y)−1)(4(3x−2y)+1)=(6x−4y−1)(12x−8y+1)
Hence, 8(3x−2y)2−6x+4y−1=(6x−4y−1)(12x−8y+1)8(3x - 2y)^2 - 6x + 4y - 1 = (6x - 4y - 1)(12x - 8y + 1)8(3x−2y)2−6x+4y−1=(6x−4y−1)(12x−8y+1).
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