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Question
Find the product of the following binomial: \[\left( \frac{4x}{5} - \frac{3y}{4} \right)\left( \frac{4x}{5} + \frac{3y}{4} \right)\]
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Solution
We will use the identity \[\left( a + b \right)\left( a - b \right) = a^2 - b^2\] in the given expression to find the product.
\[\left( \frac{4x}{5} - \frac{3y}{4} \right)\left( \frac{4x}{5} + \frac{3y}{4} \right)\]
\[ = \left( \frac{4x}{5} \right)^2 - \left( \frac{3y}{4} \right)^2 \]
\[ = \frac{16 x^2}{25} - \frac{9 y^2}{16}\]
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