# How do you multiply polynomials (a + b - c)(a + b + c)?

Mar 5, 2018

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

#### Explanation:

Note that:

$\left(A - B\right) \left(A + B\right) = {A}^{2} - {B}^{2}$

So putting $A = \left(a + b\right)$ and $B = c$ we find:

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

$\textcolor{w h i t e}{\left(a + b - c\right) \left(a + b + c\right)} = {\left(a + b\right)}^{2} - {c}^{2}$

$\textcolor{w h i t e}{\left(a + b - c\right) \left(a + b + c\right)} = {a}^{2} + 2 a b + {b}^{2} - {c}^{2}$