Question

Find the product of the following binomial: \[\left( \frac{4x}{5} - \frac{3y}{4} \right)\left( \frac{4x}{5} + \frac{3y}{4} \right)\]

Answer 1

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.

\[\left( \frac{4x}{5} - \frac{3y}{4} \right)\left( \frac{4x}{5} + \frac{3y}{4} \right)\]

\[ = \left( \frac{4x}{5} \right)^2 - \left( \frac{3y}{4} \right)^2 \]

\[ = \frac{16 x^2}{25} - \frac{9 y^2}{16}\]