simplify
(a) ${(y - 2)}^{2} - 3 (y - 2)$
(b) $5 x + 10 y - 7 {(x + 2 y)}^{2}$

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Solution

$a) (y - 2)^{2} - 3 (y - 2) = (y - 2) (y - 2 - 3) = (y - 2) (y - 5) = y^{2} - 7 y + 10 b) 5 x + 10 y - 7 (x + 2 y)^{2} = 5 (x + 2 y) - 7 (x + 2 y)^{2} = (x + 2 y) (5 - 7 x - 14 y)$

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(x^{2} - x) - \frac{1}{2} (x - 3 + 3 x^{2})

(\frac{1}{3} y^{2} - \frac{4}{7} y + 5) - (\frac{2}{7} y - \frac{2}{3} y^{2} + 2) - (\frac{1}{7} y - 3 + 2 y^{2})

25 (x - 2 y)^{2} - 4

(5 x - 10 y + 2) (5 x - 10 y - 2)

2 x + y \geq 10 x + 3 y \geq 15 x \leq 10 y \leq 8 x, y \geq 0

x + y \geq 1 10 x + y \geq 5 x + 10 y \geq 1 x, y \geq 0

Factorise: $5 x + 10 y - 7 (x + 2 y)^{2} .$

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