Simplify:
$(i) (2 y + 3) (y - 2) - (5 y + 3) (y - 2)$
$(i i) (3 x - 4 y) (x + y) - (5 x + 7 y) (x - y)$

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Solution

We have,

$(i) (2 y + 3) (y - 2) - (5 y + 3) (y - 2)$

$(i i) (3 x - 4 y) (x + y) - (5 x + 7 y) (x - y)$

$(i) (2 y + 3) (y - 2) - (5 y + 3) (y - 2)$

$\Rightarrow (2 y^{2} - 4 y + 3 y - 6) - (5 y^{2} - 10 y + 3 y - 6)$

$\Rightarrow (2 y^{2} - y - 6) - (5 y^{2} - 7 y - 6)$

$\Rightarrow 2 y^{2} - y - 6 - 5 y^{2} + 7 y + 6$

$\Rightarrow - 3 y^{2} + 6 y$

$(i i) (3 x - 4 y) (x + y) - (5 x + 7 y) (x - y)$

$\Rightarrow (3 x^{2} + 3 x y - 4 x y - 4 y^{2}) - (5 x^{2} - 5 x y + 7 x y - 7 y^{2})$

$\Rightarrow (3 x^{2} - x y - 4 y^{2}) - (5 x^{2} + 2 x y - 7 y^{2})$

$\Rightarrow 3 x^{2} - x y - 4 y^{2} - 5 x^{2} - 2 x y + 7 y^{2}$

$\Rightarrow - 2 x^{2} - 3 x y + 3 y^{2}$

Hence, this is the answer.

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