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Chapter 1: Problem 740

Simplify. $$ 9(8 w) $$

Short Answer

Expert verified
The simplified form is \( 72w \).

Step by step solution

01

Understanding the Expression

The given expression is \( 9(8w) \). It combines multiplication of constants with a variable inside the parentheses.
02

Rearrange the Terms

Rearrange the terms inside the parentheses to make the multiplication straightforward. The expression can be written as \( 9 \times 8 \times w \).
03

Multiply the Constants

Multiply the constant numbers: \( 9 \times 8 = 72 \). Thus, the expression becomes \( 72w \).

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Key Concepts

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

multiplication
Multiplication is one of the key operations in mathematics. It allows us to add groups of the same size easily, using less time and effort. In an algebraic expression like the one given, multiplication involves combining numbers and variables in a way that simplifies the overall expression.
When simplifying algebraic expressions through multiplication, follow these simple steps:
  • Identify all the numbers (constants) and variables in the expression.
  • Multiply the constants together first.
  • Keep the variable as is, unless it appears more than once.
This process ensures that the expression is simpler and easier to manage.
constants
Constants are fixed values that do not change. In algebra, they are represented by numbers without variables. For instance, in the expression given, the numbers 9 and 8 are constants.
When simplifying expressions, constants are often multiplied or added to streamline the calculation. To handle constants in an expression:
  • Locate all the constants in the equation.
  • Combine them using the appropriate operation, usually multiplication or addition.
  • In our example, the constants 9 and 8 are multiplied to get 72.
Understanding how to manipulate constants is crucial for simplifying algebraic expressions efficiently.
variables
Variables are symbols that represent unknown values in an equation. They are usually denoted by letters like 饾懃, 饾懄, or 饾懁. In our example, the variable is 饾懁.
Variables can be combined using mathematical operations, but their essence remains unchanged unless we know their specific value. Methods to work with variables:
  • Keep track of all the variables in the expression.
  • Combine like terms if there are multiple occurrences of the same variable.
  • In our particular case, we only have the variable 饾懁, so it stays as 饾懁 in the simplified expression 72饾懁.
Understanding variables is a foundational step in solving algebraic equations and simplifying expressions.

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