# Video: Pack 3 β’ Paper 3 β’ Question 16

Pack 3 β’ Paper 3 β’ Question 16

02:27

### 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.

Letβs 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¦. Youβll notice β Iβm 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¦.