Video Transcript
Write an expression for the product of the cube of 𝑥 and the difference between a
number 𝑦 and nine, all divided by two.
In this question, we want to represent a series of operations applied to multiple
variables, that is, the product of the cube of 𝑥 and the difference between a
number 𝑦 and nine all divided by two. It is important that we get the order of operations, often remembered using the
acronym PEMDAS, correct. And to do this, we need to consider the wording of the operations.
Let’s start by determining each of the factors in the product. The first factor is the cube of 𝑥, written 𝑥 cubed. And the second factor is the difference between 𝑦 and nine, written 𝑦 minus
nine. Therefore, the product of these expressions is written as 𝑥 cubed multiplied by 𝑦
minus nine. Note that we write 𝑦 minus nine inside parentheses as we need to subtract nine from
𝑦 before multiplying by 𝑥 cubed.
Let’s now consider the last few words of the question. After describing an expression, the one we have just formed, the question then tells
us that this is all divided by two. This signifies that division by two is the final operation that must be applied. Hence, we then divide this product by two to get 𝑥 cubed multiplied by 𝑦 minus nine
all over two.
