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Chapter 10: Problem 544

Multiply. $$7(10-x)$$

Short Answer

Expert verified
70 - 7x

Step by step solution

01

- Distribute the Factor

Distribute the 7 to each term inside the parentheses. This means multiplying 7 by 10 and 7 by (-x).
02

- Multiply Terms

Calculate the product of 7 and 10, which is 70. Then calculate the product of 7 and (-x), which is (-7x).
03

- Combine the Results

Combine the results from Step 2 to form the expression: (70 - 7x).

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Key Concepts

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

distributive property
The first step in solving the problem is to use the distributive property. This is a key concept in prealgebra multiplication. The distributive property states that when you multiply a number by a sum (or difference) inside parentheses, you need to multiply the number outside the parentheses by each term inside the parentheses.

In our exercise, we have the expression \(7(10 - x)\). To apply the distributive property:
  • Multiply 7 by 10 to get 70.
  • Multiply 7 by -x to get -7x.

This gives us the new expression: 70 - 7x. Remember, each term inside the parentheses gets multiplied by the number outside.
combining like terms
Combining like terms is an essential step in simplifying algebraic expressions. Like terms are terms that have the same variable raised to the same power. In prealgebra, this often involves combining constants (numbers without variables) and variable terms separately.
Let's revisit our example where we distributed the 7: 7(10 - x) which became 70 - 7x.

Here, we only have one constant term (70) and one variable term (-7x). Since there are no other like terms to combine, this expression is already simplified.
When combining like terms:
  • Add or subtract the coefficients of the variables.
  • Combine any constant terms together.
This process makes the expression easier to work with in further algebraic operations.
algebraic expressions
Understanding algebraic expressions is crucial in algebra. An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. In our exercise, we start with a simple algebraic expression \(7(10 - x)\).
Here, we have:
  • The number 7 (a coefficient)
  • The number 10 (a constant)
  • The variable x (a placeholder for an unknown value)

The steps we took transformed this initial expression into another algebraic expression 70 - 7x.
Algebraic expressions can be manipulated using properties like distributive property and combining like terms, which help in simplifying or solving equations.
Recognizing these parts and knowing how to manipulate them form the basis of solving algebra problems effectively.

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