Factorise :
(2a−3)2−2(2a−3)(a−1)+(a−1)2(2a - 3)^2 - 2(2a - 3)(a - 1) + (a - 1)^2(2a−3)2−2(2a−3)(a−1)+(a−1)2
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(2a−3)2−2(2a−3)(a−1)+(a−1)2=[(2a−3)−(a−1)]2=(2a−3−a+1)2=(a−2)2(2a - 3)^2 - 2(2a - 3)(a - 1) + (a - 1)^2 = [(2a - 3) - (a - 1)]^2\\[1em] = (2a - 3 - a + 1)^2\\[1em] = (a - 2)^2(2a−3)2−2(2a−3)(a−1)+(a−1)2=[(2a−3)−(a−1)]2=(2a−3−a+1)2=(a−2)2
Hence, (2a−3)2−2(2a−3)(a−1)+(a−1)2=(a−2)2(2a - 3)^2 - 2(2a - 3)(a - 1) + (a - 1)^2 = (a - 2)^2(2a−3)2−2(2a−3)(a−1)+(a−1)2=(a−2)2.
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