Question

Find each product.

$\left(\mathbf{2}x+\mathbf{5}y\right)\left(\mathbf{2}x-\mathbf{5}y\right)$

Short answer

$\mathbf{4}{x}^2-\mathbf{25}{y}^2$

Step-by-step solution

Step 1. Write a pattern of product of sum and difference.

The product of$x+y$ and$x-y$ is the square of x minus square of y, that is,

$$\begin{gathered} \left(x+y\right)\left(x-y\right)=\left(x-y\right)\left(x+y\right) \\ =x^2-y^2 \end{gathered}$$

Step 2. Apply pattern of product of sum and difference.

Apply the pattern of product of sum and difference to the given expression.

${\left(2x\right)}^2-{\left(5y\right)}^2$

Step 3. Simplify.

Simplify the above obtained expression.

$2^2{x}^2-5^2{y}^2=4x^2-25y^2$

Therefore, the product of$\left(2x+5y\right)\left(2x-5y\right)$ is $4x^2-25y^2$.