# How do you find the product (a-2b)^2?

Apr 5, 2017

${a}^{2} - 4 a b + 4 {b}^{2}$

#### Explanation:

Note: ${\left(a - 2 b\right)}^{2} = \left(a - 2 b\right) \left(a - 2 b\right)$

Each term in the second bracket must be multiplied by each term in the first bracket. This is shown below.

$\left(\textcolor{red}{a - 2 b}\right) \left(a - 2 b\right)$

$= \textcolor{red}{a} \left(a - 2 b\right) \textcolor{red}{- 2 b} \left(a - 2 b\right)$

distribute and collect like terms.

$= {a}^{2} \textcolor{m a \ge n t a}{- 2 a b} \textcolor{m a \ge n t a}{- 2 a b} + 4 {b}^{2}$

$= {a}^{2} - 4 a b + 4 {b}^{2}$