# How do you find the product (2x+7y)^2?

##### 1 Answer
Apr 15, 2018

$4 {x}^{2} + 49 {y}^{2} + 28 x y$

#### Explanation:

Product simply means multiply:

${\left(2 x + 7 y\right)}^{2} \to \left(2 x + 7 y\right) \left(2 x + 7 y\right)$

Using FOIL or an alternative method:

$\left(\textcolor{red}{2 x} \textcolor{b l u e}{+ 7 y}\right) \left(\textcolor{red}{2 x} \textcolor{b l u e}{+ 7 y}\right)$

color(red)(2x) xx color(red)(2x=4x^2

$\textcolor{red}{2 x} \times \textcolor{b l u e}{7 y} = \textcolor{g r e e n}{14 x y}$

$\textcolor{b l u e}{7 y} \times \textcolor{red}{2 x} = \textcolor{g r e e n}{14 x y}$

$\textcolor{b l u e}{7 y} \times \textcolor{b l u e}{7 y} = \textcolor{b l u e}{49 {y}^{2}}$

Collecting like terms:

$\textcolor{red}{4 {x}^{2}} + \textcolor{b l u e}{49 {y}^{2}} + \textcolor{g r e e n}{14 x y} + \textcolor{g r e e n}{14 x y} \to \textcolor{red}{4 {x}^{2}} + \textcolor{b l u e}{49 {y}^{2}} + \textcolor{g r e e n}{28 x y}$

This is the final answer.

Remember you can always factorise this to check.