Writing Mathematical Expressions: Difference and Product

As an excellent high school mathematics teacher, I'm excited to share with you a detailed approach to writing an expression that represents the difference of y and 32, plus the product of y and 4.

Understanding the Problem

The expression we need to write is made up of two parts:

1. The difference of y and 32
2. The product of y and 4

To represent this expression, we can use mathematical symbols and variables.

Step 1: Represent the Difference

The difference of y and 32 can be written as:

y - 32

This expression subtracts 32 from the variable y.

Step 2: Represent the Product

The product of y and 4 can be written as:

y × 4 or y * 4

This expression multiplies y by the constant 4.

Step 3: Combine the Expressions

To combine the difference and the product, we can use the addition operator (+):

(y - 32) + (y * 4)

This expression represents the difference of y and 32, plus the product of y and 4.

Simplifying the Expression

If we want to simplify the expression further, we can combine the terms with the variable y:

y - 32 + 4y 5y - 32

The final expression that represents the difference of y and 32, plus the product of y and 4, is 5y - 32.

Remember, the ability to write and manipulate mathematical expressions is a fundamental skill in mathematics. By understanding the step-by-step process, you can tackle more complex expressions with confidence.