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Chapter 1: Problem 741

Simplify. $$ -15(5 m) $$

Short Answer

Expert verified
-75m

Step by step solution

01

- Identify the terms

Look at the expression a. Identify the constant term -15, b. and the variable term 5m (which is 5 multiplied by m).
02

- Multiply the constants

Multiply the constants together, which are -15 and 5. a. -15 * 5 = -75.
03

- Combine the product with the variable

Attach the variable m to the product obtained from Step 2. a. This gives -75m.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

constant term
A constant term is a value that does not change. It stands alone and does not have a variable attached. For example, in the expression ewline -15(5m), the -15 is the constant term. No matter what happens to the variable, the constant term remains the same. It's like a number on its own.
variable term
Variable terms are numbers that contain variables. A variable is usually represented by letters like m, x, or y. In the expression 5m, the number 5 is multiplied by the variable m. Here, 5m changes as the value of m changes. The variable term can change based on what we substitute the variable with.
multiplication of constants
When simplifying expressions, sometimes you need to multiply constants. In our example, the constants are -15 and 5. You multiply them just like regular numbers: \[ -15 \times 5 = -75 \] Once you have the product of the constants, you can move on to the next step. This multiplication simplifies the constant part of the expression.
combining like terms
Combining like terms means simplifying an expression by adding or subtracting terms that have the same variable part. In the given exercise, we can combine the product of the constants with the remaining variable.The last step is to attach the variable m to the product you obtained from multiplying the constants:The expression \[ -75 \times m \] is simplified to \[ -75m \]. This final form is more straightforward and easy to work with.

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