Question

Factor completely: Z to the power of 3 - 16z?

Answer 1

`=>z ( z-4)(z+4)`

Explanation:

`z^3 - 16z`

First factor out the common `z`

`=> z(z^2 - 16 )`

Use the difference in two squares...

`(a^2-b^2) = (a-b)(a+b)`

`=>color(red)(z ( z-4)(z+4)`

Answer 2

`z(z-4)(z+4)`

Explanation:

`"take out a "color(blue)"common factor "z`

`rArrz^3-16z=z(z^2-16)`

`z^2-16" is a "color(blue)"difference of squares"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`"here "a=z" and "b=4`

`rArrz^2-16=(z-4)(z+4)`

`rArrz^3-16z=z(z-4)(z+4)`