How do you find the product of (x-y)(x^2+xy+y^2)(x−y)(x2+xy+y2)?
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))x(x2+xy+y2)−y(x2+xy+y2) now distribute the brackets.
x^3+x^2y+xy^2-x^2y-xy^2-y^3x3+x2y+xy2−x2y−xy2−y3 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"
