How do you find the product #(q+r)^2(q-r)#?

1 Answer
Jan 20, 2017

Answer:

#q^3 + q^2r - qr^2 - r^3#

Explanation:

We are asked to find the product of two numbers #(q + r)^2# and #(q - r)#. The algebraic expressions #(q + r)# and #(q - r)# reflect the internal structure of each number.
We can think of #(q + r)^2# as equal to #(q + r) ##(q + r)#

So #(q + r)^2 ##(q - r)# = #(q + r) ##(q + r)# #(q - r)#

We should be familiar with the result

#(q + r) ##(q - r)#= #(q^2 - r^2)#

So #(q + r) ##(q + r)# #(q - r)#= #(q^2 - r^2)##( q + r)#

And multiplying out in full

#(q^2 - r^2)##( q + r)#= #q^3 + q^2r - qr^2 - r^3#