Question

Find the product.

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

Short answer

The final answer is $\mathbf{4}{\mathit{r}}^{\mathbf{2}}\mathbf{+}\mathbf{20}\mathit{r}\mathit{t}\mathbf{+}\mathbf{25}{\mathit{t}}^{\mathbf{2}}$.

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.

$\begin{array}{c}{\left(2r+5t\right)}^2={\left(2r\right)}^2+2\left(2r\right)\left(5t\right)+{\left(5t\right)}^2\\ ={\left(2\right)}^2{\left(r\right)}^2+20rt+{\left(5\right)}^2{\left(t\right)}^2\\ =4r^2+20rt+25t^2\end{array}$

Therefore, the final answer is $4r^2+20rt+25t^2$.