# How do you multiply (x + y)(x + y)?

Mar 17, 2017

See a couple of solution processes below:

#### Explanation:

This is an example of the perfect square. The formula for this is:

$\left(a + b\right) \left(a + b\right) = {a}^{2} + 2 a b + {b}^{2}$

Substituting $x$ for $a$ and $y$ for $b$ gives:

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

Another way to show this is the correct answer is as follows:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

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

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

${x}^{2} + x y + x y + {y}^{2}$

We can now combine like terms:

${x}^{2} + 1 x y + 1 x y + {y}^{2}$

${x}^{2} + \left(1 + 1\right) x y + {y}^{2}$

${x}^{2} + 2 x y + {y}^{2}$