Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Factor completely, then place the answer in the proper location on the grid. x 3 - y 3

Answer 1

The factors of
`x^(3)-y^(3)` are
`[(x-y)(x^(2)+xy+y^(2))]`.

Explanation:

We know that:

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

Compute the factors of
`x^(3)-y^(3)` as follows:

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

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

Thus, the factors of
`x^(3)-y^(3)` are
`[(x-y)(x^(2)+xy+y^(2))]`.