### Video Transcript

The area of the floor of a silo is
two π₯ plus nine squared square feet. The height of the silo is 10π₯ plus
10 feet. Write an expression for the volume
of grain that the silo can hold by expanding the square and multiplying by the
height.

So we are to find the volume of the
silo. And volume has a formula the area
of the base times the height. And we know that the area of the
floor of the silo, which would be the base, is equal to two π₯ plus nine squared
square feet. And then the height we know to be
10π₯ plus 10 feet.

So it told us to find the volume of
grain that the silo can hold by expanding the square β so we will be expanding this
square β and then multiplying by the height. So we will do exactly that.

Now we wonβt keep writing feet
squared and feet. If we know that our answer should
have feet squared times feet, that would be feet cubed. And that makes sense because a
volume should be cubic feet. So we will add that to the end.

So we will first begin to expand by
writing two π₯ plus nine twice, instead of writing it as squared. So now we need to FOIL,
distribute. Two π₯ times two π₯ is four π₯
squared. Two π₯ times nine is 18π₯. Nine times two π₯ is 18π₯. And then nine times nine is 81. So we could keep multiplying by the
10π₯ plus 10.

However, letβs condense inside the
pink parentheses, because we can actually combine 18π₯ and 18π₯. So now weβve combined them, we need
to FOIL again, distribute. Four π₯ squared times 10π₯ is 40π₯
cubed. Four π₯ squared times 10 is equal
to 40π₯ squared. 36π₯ times 10π₯ is equal to 360π₯
squared. 36π₯ times 10 is equal to
360π₯. 81 times 10π₯ is equal to
810π₯. And 81 times 10 is equal to
810.

Now we need to combine like terms,
and they will be simplified. So our highest exponent is
three. We have 40π₯ cubed, and that should
be written first. Our next highest power is π₯
squared. And we have 40π₯ squared and 360π₯
squared that we can combine, giving us 400π₯ squared. Next, our next highest power is
just π₯ to the first power. And when we add them together, we
get 1170π₯. And then, lastly, we have the
constant of 810. So this will be our final
answer.

However, we need to add feet
cubed. Now instead of just writing feet
cubed at the end, it kind of just looks like the feet cubed goes with 810. So if we have more than one term,
itβs good to put parentheses around it so to emphasize that the entire thing is
cubic feet. So this will be our final
answer.