Factorise:

$(2 a - 3)^{2} - 2 (2 a - 3) (a - 1) + (a - 1)^{2}$

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Solution

$(2 a - 3)^{2} - 2 (2 a - 3) (a - 1) + (a - 1)^{2} [U s e a^{2} + b^{2} - 2 a b = (a - b)^{2}] \Rightarrow [(2 a - 3) - (a - 1)]^{2} \Rightarrow [2 a - 3 - a + 1]^{2} \Rightarrow (a - 2)^{2}$

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