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

1 Answer
Jul 5, 2016

Answer:

#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)#