Question

Find the product.

${\left(5x+4\right)}^{\mathbf{2}}$

Short answer

The final answer is $\mathbf{25}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{40}\mathit{x}\mathbf{+}\mathbf{16}$.

Step-by-step solution

Step 1. Define an expression.

A mathematical expression is a combinations of numbers and variables ordered with mathematical operations.

Step 2. Expand the identity, (a+b)2.

${\left(a+b\right)}^2=a^2+2ab+b^2\dots \dots \dots .\left(1\right)$

Step 3. Calculate the product (5x+4)2.

Use equation (1) to find the product.

$\begin{array}{c}{\left(5x+4\right)}^2={\left(5x\right)}^2+2\left(5x\right)\left(4\right)+4^2\\ ={\left(5\right)}^2{\left(x\right)}^2+40x+16\\ =25x^2+40x+16\end{array}$

Therefore, the final answer is $25x^2+40x+16$.