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Power of a Power

Simplify: 4m2...

Question

$Simplify: \frac{4 m^{2} - 169 n^{2}}{2 m + 13 n}$

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Solution

$Simplify: \frac{4 m^{2} - 169 n^{2}}{2 m + 13 n} = \frac{(2 m)^{2} - (13 n)^{2}}{2 m + 13 n}$

$Using the identity a^{2} - b^{2} = (a + b) (a - b)$

$\Rightarrow \frac{(2 m)^{2} - (13 n)^{2}}{2 m + 13 n} = \frac{(2 m - 13 n) (2 m + 13 n)}{2 m + 13 n}$

$= 2 m - 13 n$

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