# How do you find the product (11-a)^2?

May 13, 2017

color(brown)(a^2-22a+121

#### Explanation:

$\textcolor{w h i t e}{a a a a a a a a a a a a}$$11 - a$
$\textcolor{w h i t e}{a a a a a a a a a a}$$\underline{\times 11 - a}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$121 - 11 a$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a}$$\underline{- 11 a + {a}^{2}}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a}$$121 - 22 a + {a}^{2}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a}$color(brown)(a^2-22a+121

May 13, 2017

$121 - 22 a + {a}^{2}$

#### Explanation:

$\text{express } {\left(11 - a\right)}^{2} = \left(11 - a\right) \left(11 - a\right)$

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

$\left(\textcolor{red}{11 - a}\right) \left(11 - a\right)$

$= \textcolor{red}{11} \left(11 - a\right) \textcolor{red}{- a} \left(11 - a\right)$

$= \left(\textcolor{red}{11} \times 11\right) + \left(\textcolor{red}{11} \times - a\right) + \left(\textcolor{red}{- a} \times 11\right) + \left(\textcolor{red}{- a} \times - a\right)$

$= 121 - 11 a - 11 a + {a}^{2}$

$= 121 - 22 a + {a}^{2}$