Look for the function rule. Essentially, this function takes the first number, multiplies it by the second number, and then subtracts the first number.

First evaluate (y # z) since it is the inner function.

Since x # y = xy � x, substitute y for x and z for y.

So y # z = yz � y.

Now substitute yz � y into the function.

x # (y # z) = x # (yz � y)

Apply the function rule:

take the first number: x

multiply it by the second number: (yz � y)

then subtract the first number: x

x # (yz � y) = x � (yz � y) � x = xyz � xy � x

Depending on the answer choices, you may need to factor out the x.

xyz � xy � x = x(yz � y � 1)

**Checking**

One method to check your answer is to Plug In some numbers.

Choose some numbers for the variables. Let x = 1, y = 3 and z = 2.

x # (y # z) = 1 # (3 # 2)

Now use these numbers and apply the rule x # y = xy � x.

Do the inner function first and evaluate (3 # 2).

Since x # y = xy � x, substitute 3 for the first variable and 2 for the second variable.

x # y = xy � x becomes (3)(2) � 3 = 3

So 1 # (3 # 2) becomes 1 # 3.

Since x # y = xy � x, substitute 1 for the first variable and 3 for the second variable.

x # y = xy � x becomes (1)(3) � 1 = 2

Check your answer by using the values x = 1, y = 3 and z = 2.

x # (y # z) = xyz � xy � x becomes (1)(2)(3) � (1)(3) � 1 = 6 � 3 � 1 = 2.

Since these values match the variables in the expression you found, you can infer that your expression is correct.