# How do you multiply (a-b)(a-b)?

Aug 7, 2015

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

#### Explanation:

We multiply each term as follows

$a \left(a\right) + \left(a\right) \left(- b\right) + \left(- b\right) \left(a\right) + \left(- b\right) \left(- b\right)$

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

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

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

Or you can use the FOIL method. This is the same thing but just visualizing differently.

FOIL stands for

First Outside Inside Last

First multiply the first terms in $\left(a - b\right) \left(a - b\right)$
$a \left(a\right) = {a}^{2}$

Now add the products of the Outside and Inside terms

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

Finally we add the product of the last terms

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