Question

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

Answer 1

`ab^(2x+1)(ab-1)`

Explanation:

Using the following `color(blue)"law of exponents"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(a^mxxa^nhArra^(m+n))color(white)(a/a)|)))`

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

Note then that `b^(2x+2)=b^(2x)xxb^2,b^(2x+1)=b^(2x)xxb`

Hence the common factors of the expression are

`a b^(2x)b(ab-1)=ab^(2x+1)(ab-1)`