How do you simplify (5 - 8y)^2?

Apr 27, 2017

$64 {y}^{2} - 80 y + 25$

Explanation:

Each term in the second bracket is multiplied by each term in the first bracket as shown below.

${\left(5 - 8 y\right)}^{2} = \left(5 - 8 y\right) \left(5 - 8 y\right)$

$\Rightarrow \left(\textcolor{red}{5 - 8 y}\right) \left(5 - 8 y\right)$

$= \textcolor{red}{5} \left(5 - 8 y\right) \textcolor{red}{- 8 y} \left(5 - 8 y\right)$

$= \left(\textcolor{red}{5} \times 5\right) + \left(\textcolor{red}{5} \times - 8 y\right) + \left(\textcolor{red}{- 8 y} \times 5\right) + \left(\textcolor{red}{- 8 y} \times - 8 y\right)$

$= 25 + \left(- 40 y\right) + \left(- 40 y\right) + 64 {y}^{2}$

$= 25 - 40 y - 40 y + 64 {y}^{2}$

$= 64 {y}^{2} - 80 y + 25 \leftarrow \textcolor{red}{\text{ in standard form}}$