# How do you factor the expression (a^2) b^(2x+ 2) - (a) b^(2x+1)?

Jul 5, 2016

$a {b}^{2 x + 1} \left(a b - 1\right)$

#### Explanation:

Using the following $\textcolor{b l u e}{\text{law of exponents}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{a}^{m} \times {a}^{n} \Leftrightarrow {a}^{m + n}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

If the 'bases' (a) of the product are equal then add the exponents.

Note then that ${b}^{2 x + 2} = {b}^{2 x} \times {b}^{2} , {b}^{2 x + 1} = {b}^{2 x} \times b$

Hence the common factors of the expression are

$a {b}^{2 x} b \left(a b - 1\right) = a {b}^{2 x + 1} \left(a b - 1\right)$