Factorise the expression and divide them as directed: $12 x y (9 x^{2} - 16 y^{2}) \div 4 x y (3 x + 4 y)$ .

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Solution

Step 1: Factorize the expression $12 x y (9 x^{2} - 16 y^{2})$ .
Using identity $(a^{2} - b^{2}) = (a + b) (a - b)$ , expand the above expression.
$\Rightarrow 12 x y ({(3 x)}^{2} - {(4 y)}^{2}) = 12 x y (3 x + 4 y) (3 x - 4 y)$
Step 2: Divide the expression by $4 x y (3 x + 4 y)$ to get the final answer.
$\Rightarrow \frac{12 x y (3 x + 4 y) (3 x - 4 y)}{4 x y (3 x + 4 y)} \Rightarrow 3 (3 x - 4 y)$
Hence, the required final answer is $3 (3 x - 4 y)$ .

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