Factorise : $2 (x + 2 y)^{2} - 5 (x + 2 y) + 2$

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Solution

$2 (x + 2 y)^{2} - 5 (x + 2 y) + 2 L e t x + 2 y = a, t h e n 2 a^{2} - 5 a + 2 \Rightarrow 2 a^{2} - a - 4 a + 2 = a (2 a - 1) - 2 (2 a - 1) = (2 a - 1) (a - 2) = {2 (x + 2 y - 1)} {(x + 2 y) - 2} = (2 x + 4 y - 2) (x + 2 y - 2) ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} ∵ 2 \times 2 = 4 - 5 = - 1 - 4 4 = (- 1) \times (- 4) \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭$

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