Question

Simplify [(16a2 – 81b2

)/(4a – 9b)]​

Answer 1

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$\sf{simplify : } \\ \sf{ \frac{16a {}^{2} - 81b {}^{2} }{4a - 9b } }$

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$\\ \sf{ \frac{16a {}^{2} - 81b {}^{2} }{4a - 9b } } \\ \\ \sf{ = \frac{(4a) {}^{2} - (9b) {}^{2} }{(4a - 9b)} } \\ \\ \sf{by \: using \: identity \: :} \\ \\ \sf{a {}^{2} - b {}^{2} = (a + b)(a - b)} \\ \\ \sf{ = \frac{(4a - 9b)(4a + 9b)}{(4a - 9b)} } \\ \\ \sf{ = \frac{ \cancel{(4a - 9b)}(4a + 9b)}{ \cancel{(4a - 9b)}} } \\ \\ \bold{ \underline{ \underline{ \sf{ = (4a + 9b)}}}}$