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

1 Answer
Jan 20, 2017

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