### Video Transcript

Factor the expression four ππ
plus two ππ completely.

In this question, we are given an
algebraic expression that we are asked to factor completely. This means that we need to find
every nontrivial common factor among the terms so that we cannot factor any
further.

To do this, letβs check for common
factors among the coefficients and variables separately. We can start by checking for the
greatest common divisor of the coefficients. We can note that the greatest
common divisor of four and two is two. So we can take out a common factor
of two out of the expression.

We can also check for common
factors among the variables. We note that the first term only
has factors of π and π. So we check the second term for
these factors. We see that the second term has a
factor of π but not π. So we can take out a factor of π
from the expression. We call two π the greatest common
factor of the terms, since we cannot take out any more factors from the terms. We can then take this factor out to
obtain two π times two π plus π.

We can then check that we cannot
factor the expression any further to confirm that the expression is fully
factored. Hence, our answer is two π
multiplied by two π plus π.