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

##### 1 Answer

Oct 19, 2016

#### 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"#