Question

Find each product.

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

Short answer

$x^2+\mathbf{10}x+\mathbf{25}$

Step-by-step solution

Step 1. Write a pattern of square of a sum.

The square of$x+y$ is the square of x plus twice the product of x and y plus square of y, that is,

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

Step 2. Apply pattern of square of sum.

Apply the pattern of square of sum to the given expression.

$x^2+2\cdot x\cdot 5+5^2$

Step 3. Simplify.

Simplify the above obtained expression.

$x^2+10x+25$

Therefore, the product of${\left(x+5\right)}^2$ is $x^2+10x+25$.