Question

Factor fully.
a)5m^3 - 40m^2 + 80m
Answer: 5m(m-4)^2 <- how to get this?

Answer 1

First you should notice every term in \(5m^3-40m^2+80m\) can be evenly divided by \(5m\), so you can factor it out: \(5m(m^2-8m+16)\). Next, notice we can expand our quadratic trinomial factor \(m^2-8m+16\) into \(m^2-4m-4m+16\); it should be clear you can factor this into \(m(m-4)-4(m-4) = (m-4)(m-4)=(m-4)^2\). This means our final factored form is \(5m(m-4)^2\).