### Video Transcript

Write an expression for double the square of π₯, which is then divided by nine less
than the cube of π¦.

In this question, we want to represent a series of operations applied to multiple
given variables. When dealing with any problem of this type, it is important that we get the order of
operations correct. The first part of the relationship says, βDouble the square of π₯.β We begin by squaring the variable, which we write as π₯ squared. We then need to double the expression. We note that in the order of operations, exponentiation is carried out before
multiplication, so we can write this as two π₯ squared.

Now letβs consider the second part of the relationship: nine less than the cube of
π¦. We need to cube π¦, written π¦ cubed. Then, we need to decrease this value by nine. Since subtraction is carried out after exponentiation, this can be written as π¦
cubed minus nine.

Finally, we need to divide the first expression by the second expression, which gives
us two π₯ squared divided by π¦ cubed minus nine. It is worth noting that whilst we could put both the numerator and denominator in
parentheses, this is not required, since it is convention to evaluate the numerator
and the denominator of the quotient first before carrying out the division
operation.

We can therefore conclude that the correct expression is two π₯ squared over π¦ cubed
minus nine.