Simplify the following
$(2 x - 3 y) (3 x + y) + (x + 2 y) (x - y)$ .

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Solution

Given expression is $(2 x - 3 y) (3 x + y) + (x + 2 y) (x - y)$

Simplifying the expression by multiplying the terms as per the given operation,

$[2 x (3 x + y) - 3 y (3 x + y)] + [x (x - y) + 2 y (x - y)]$

$\Rightarrow [6 x^{2} + 2 x y - 9 x y - 3 y^{2}] + [x^{2} - x y + 2 x y - 2 y^{2}]$

$\Rightarrow [6 x^{2} - 3 y^{2} - 7 x y] + [x^{2} - 2 y^{2} + x y]$

$\Rightarrow 6 x^{2} - 3 y^{2} - 7 x y + x^{2} - 2 y^{2} + x y$

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

Hence, $(2 x - 3 y) (3 x + y) + (x + 2 y) (x - y) = 7 x^{2} - 5 y^{2} - 6 x y$ .

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