### Video Transcript

By taking out the HCF, factor
the expression 14π₯ to the fifth power π¦ squared minus four π₯ cubed π¦ plus
eight π₯ squared π¦.

Weβre given the expression 14π₯
to the fifth power π¦ squared minus four π₯ cubed π¦ plus eight π₯ squared π¦,
and we need the HCF, the highest common factor. Weβll start by considering the
highest common factor of the coefficients of these three terms. 14 equals two times seven. Four equals two times two. And eight equals two times
four. The common factor here is
two. It is true that eight and four
share a factor of four, but 14 is not divisible by four. And so, we say that the common
factor for all three coefficients is two. And that means weβll rewrite
the expression as two times seven π₯ to the fifth power π¦ squared minus two π₯
cubed π¦ plus four π₯ squared π¦.

From here, we consider the
common factor of π₯. The third term has the smallest
factor of π₯, π₯ squared, which means π₯ squared is the biggest factor of π₯ we
can remove. So, weβll undistribute a factor
of π₯ squared from these three terms. π₯ to the fifth power divided
by π₯ squared equals π₯ cubed. And we leave the π¦
squared. π₯ cubed divided by π₯ squared
equals π₯ to the first power. And four π₯ squared π¦ divided
by π₯ squared will be equal to four π¦. We now have a second equivalent
expression. However, we still do not have
our highest common factor. And we know this because all
three of our terms have at least one factor of π¦. The smallest factor of π¦ here
is π¦ to the first power. And that means thatβs the most
we can remove from all three terms. We undistribute π¦ to the first
power from all three terms.

Our first term becomes seven π₯
cubed π¦ to the first power. Our second term is then
negative two π₯ to the first power. When we remove a factor of π¦
to the first power from our third term, weβre just left with four. What we see now is that there
are no common factors in the parentheses. And that means the highest
common factor is what weβve taken out. By undistributing the highest
common factor two π₯ squared π¦, we have a fully factorized expression, two π₯
squared π¦ times seven π₯ cubed π¦ minus two π₯ plus four. If you wanted to check if this
was true, you would multiply the highest common factor back by the three
remaining terms, which would give you the expression you started with.