# How do you multiply (5n-4)^2?

Jun 9, 2017

$25 {n}^{2} - 40 n + 16$

#### Explanation:

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

${\left(5 n + \left(- 4\right)\right)}^{2} = {\left(5 n\right)}^{2} + 2 \cdot 5 n \cdot \left(- 4\right) + {\left(- 4\right)}^{2}$

Jun 9, 2017

$25 {n}^{2} - 40 n + 16$

#### Explanation:

$\text{express } {\left(5 n - 4\right)}^{2} = \left(5 n - 4\right) \left(5 n - 4\right)$

$\text{each term in the second bracket is multiplied by each term}$
$\text{in the first bracket as shown below}$

$\left(\textcolor{red}{5 n - 4}\right) \left(5 n - 4\right)$

$= \textcolor{red}{5 n} \left(5 n - 4\right) \textcolor{red}{- 4} \left(5 n - 4\right)$

$\text{distributing gives}$

$= \left(\textcolor{red}{5 n} \times 5 n\right) + \left(\textcolor{red}{5 n} \times - 4\right) + \left(\textcolor{red}{- 4} \times 5 n\right) + \left(\textcolor{red}{- 4} \times - 4\right)$

$= 25 {n}^{2} - 20 n - 20 n + 16 \leftarrow \text{ collect like terms}$

$= 25 {n}^{2} - 40 n + 16$