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Chapter 15: Problem 63

Multiply. $$ -2(15-3 x) $$

Short Answer

Expert verified
-30 + 6x

Step by step solution

01

- Distribute the -2

Distribute the -2 to each term inside the parentheses. This means you will multiply -2 by both 15 and -3x.
02

- Multiply -2 by 15

Multiply -2 by 15 to get \[ -2 \times 15 = -30 \]
03

- Multiply -2 by -3x

Multiply -2 by -3x to get \[ -2 \times (-3x) = 6x \]
04

- Write the final expression

Combine the results from Step 2 and Step 3 to write the final expression: \[ -30 + 6x \]

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Key Concepts

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

algebraic expressions
An algebraic expression is a combination of numbers, variables (like x or y), and mathematical operators (such as +, -, 脳, 梅). For example, the expression -2(15-3x) involves a multiplication, a subtraction, and a variable.

One common task is to simplify algebraic expressions. This often means combining like terms or using the distributive property. In our exercise, we simplified the expression by distributing -2 across each term inside the parentheses. This made the expression easier to work with and understand.

Simplifying expressions helps solve equations and tackle complex math problems more effectively.
multiplication
Multiplication is one of the four fundamental arithmetic operations. It involves adding a number to itself a certain number of times. For example, 4 multiplied by 3 is the same as adding 4 three times: \[ 4 \times 3 = 4 + 4 + 4 = 12 \]

In algebra, multiplication can include variables. For instance, multiplying 3 by x gives \[ 3x \], which means adding x three times. In our exercise, we multiplied -2 by both 15 and -3x.

Understanding multiplication is crucial for working with algebraic expressions and equations effectively.
negative numbers
Negative numbers are numbers less than zero. They are represented with a minus sign (-). For example, -5 is a negative number. Negative numbers are used to represent loss, decrease, or opposite directions.

When dealing with negative numbers in multiplication, there are some key rules to remember:
  • Multiplying two positive numbers gives a positive result: \[ 2 \times 3 = 6 \]
  • Multiplying a positive number by a negative number gives a negative result: \[ 2 \times (-3) = -6 \]
  • Multiplying two negative numbers gives a positive result: \[ (-2) \times (-3) = 6 \]

In our exercise, these rules helped us correctly multiply -2 by both 15 and -3x, which resulted in -30 and 6x, respectively.

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