How do you find the product #(n-p)^2(n+p)#?

1 Answer
Jun 23, 2017

Answer:

#n^3-np^2-n^2p+p^3#

Explanation:

We can write #(n-p)^2# as #(n-p)(n-p)#:

#(n-p)^2(n+p)=(n-p)(n-p)(n+p)#

We can group #(n-p)# and #(n+p)# and multiply those, since they will result in a difference of squares, which is only two terms instead of three. That will make our future distribution easier.

#=(n-p){(n-p)(n+p)}=(n-p)(n^2-p^2)#

Now distribute:

#=n(n^2-p^2)-p(n^2-p^2)#

#=n^3-np^2-n^2p+p^3#