Question

How do you find the product of `(x-y)(x^2+xy+y^2)`?

Answer 1

`x^3-y^3`

Explanation:

We must ensure that each term in the second bracket is multiplied by each term in the first bracket.
This can be achieved as follows.

`color(red)(x)(color(blue)(x^2+xy+y^2))color(red)(-y)(color(blue)(x^2+xy+y^2))`

now distribute the brackets.

`x^3+x^2y+xy^2-x^2y-xy^2-y^3`

collect like terms.

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

`=x^3-y^3larr" a difference of cubes"`