How to simplify 200m^4 + 80m^3 + 8m^2?

Expert Answers
hala718 eNotes educator| Certified Educator

Given the expression E = 200m^4 + 80m^3 + 8m^2.

We need to simplify as mush as possible.

First we will need to factor all terms is order to find a common factor.

Let us factor each term.

200m^4 = 2*2*2*5*5*m*m*m*m

80m^3 = 2*2*2*2*5*m*m*m

8m^2 = 2*2*2*m*m

Now we notice that the common factor is 2*2*2*m*m = 8m^2.

Then, we will factor 8m from all terms.

==> E = 8m^2(25m^2 + 10m + 1)

Now we will factor between brackets.

==> E = 8m^2 ( 5m+1)^2

==> E = 8[m(5m+1)]^2