Question

If `x` and `y` are positive integers, how do you simplify `(2x ) ^ { 3y } - ( 2x ) ^ { y}`?

Answer 1

`(2x)^(3y)-(2x)^y=(2x)^y((2x)^y+1)((2x)^y-1)`

Explanation:

`(2x)^(3y)-(2x)^y`

= `(2x)^(y+2y)-(2x)^y`

= `(2x)^yxx(2x)^2y-(2x)^y`

= `(2x)^y((2x)^(yxx2)-1)`

= `(2x)^y(((2x)^y)^2-1^2)`

= `(2x)^y((2x)^y+1)((2x)^y-1)`