Factorise the following expressions:-
$(a x + b y)^{2} - (b x + a y)^{2}$

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Solution

$(a x + b y)^{2} - (b x + a y)^{2} a^{2} - b^{2} = (a + b) (a - b)$
$\Rightarrow (a x + b y + b x + a y) (a x + b y - b x - a y)$
$\Rightarrow (a (x + y) + b (x + y)) (a (x - y) - b (x - y))$
$\Rightarrow ((x + y) (a + b)) ((x - y) (a - b))$
$\Rightarrow [(x + y) (x - y) (a + b) (a - b)]$
$\Rightarrow [x^{2} - y^{2}] [a^{2} - b^{2}]$

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