# How do you multiply (n+5)^2?

Feb 26, 2017

See the entire solution process below:

#### Explanation:

Solution 1) You can use the formula: ${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

Substituting $n$ for $a$ and $5$ for $b$ gives:

${\left(n + 5\right)}^{2} = {n}^{2} + 2 \left(n 5\right) + {5}^{2} = {n}^{2} + 10 n + 25$

Solution 2) To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{n} + \textcolor{red}{5}\right) \left(\textcolor{b l u e}{n} + \textcolor{b l u e}{5}\right)$ becomes:

$\left(\textcolor{red}{n} \times \textcolor{b l u e}{n}\right) + \left(\textcolor{red}{n} \times \textcolor{b l u e}{5}\right) + \left(\textcolor{red}{5} \times \textcolor{b l u e}{n}\right) + \left(\textcolor{red}{5} \times \textcolor{b l u e}{5}\right)$

${n}^{2} + 5 n + 5 n + 25$

We can now combine like terms:

${n}^{2} + \left(5 + 5\right) n + 25$

${n}^{2} + 10 n + 25$