### Video Transcript

Simplify fully root two π₯ minus
root nine π¦ multiplied by root two π₯ plus three root π¦.

Before we expand the brackets, we
notice that we can in fact simplify one of the terms within the bracket. Root nine π¦ is equal to the square
root of nine multiplied by the square root of π¦. And as nine is a square number, its
square root is the integer three. Root nine π¦ is, therefore, equal
to three root π¦.

The product, therefore, becomes
root two π₯ minus three root π¦ multiplied by root two π₯ plus three root π¦. And we notice that the two brackets
are almost identical. They just have different signs
between the terms.

Letβs now expand the brackets using
the FOIL method. F stands for first, the first term
in each bracket. So we have root two π₯ multiplied
by root two π₯. This gives root two π₯ all squared,
which simplifies to two π₯ as the square root and the squared cancel each other
out.

Next, we multiply the outer terms
of the two brackets together. So we have positive root two π₯
multiplied by positive three root π¦. This gives three root two π₯π¦.

Next, we multiply the inner terms
of the two brackets together. So we have negative three root π¦
multiplied by root two π₯. This simplifies to give negative
three root two π₯π¦.

Finally, we multiply the last term
in the two brackets together. So we have negative three root π¦
multiplied by three root π¦. Negative three multiplied by three
is negative nine and root π¦ multiplied by root π¦ is π¦. So this term simplifies to negative
nine π¦.

Adding the four terms from the
expansion together, we have two π₯ plus three root two π₯π¦ minus three root two
π₯π¦ minus nine π¦. Youβll notice β Iβm sure β that the
two central terms are identical, but with different signs. And therefore, they cancel each
other out. And this is because the two
brackets were almost identical, but with different signs.

The full expansion simplifies to
just two π₯ minus nine π¦.