Problem 56 Multiply. $$ (x-2) 3 $$... [FREE SOLUTION]

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Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 5: Problem 56

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

Short Answer

Expert verified

The product is $3x - 6$.

Step by step solution

Understand the Problem

We need to multiply the expression (x - 2) by 3. This involves distributing the 3 to each term inside the parentheses.

Distribute the 3

Apply the distributive property: multiply each term within the parentheses by 3. This means we calculate 3 imes (x - 2) which gives us 3 imes x and 3 imes -2 .

Calculate Each Multiplication

First, multiply the variable term: $3 imes x = 3x$. Then multiply the constant term: $3 imes -2 = -6$.

Combine the Results

Combine the terms obtained from the distribution: $3x - 6$. This is the simplified expression after multiplying.

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Key Concepts

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

Algebraic Expressions

Algebraic expressions are a fundamental part of mathematics that help to describe relationships using variables and constants. A typical algebraic expression can consist of numbers, variables such as $x$ or $y$, and arithmetic operations like addition, subtraction, multiplication, and division.
To better understand how these expressions work, think of them as sentences where numbers and variables work together under specific rules. In the exercise, $(x - 2)$ is an algebraic expression that involves subtraction between a variable $x$ and the constant 2.

Multiplication in Algebra

Multiplication in algebra is not much different from regular multiplication, but it includes combining numbers and variables in expressions. When multiplying an expression, each term must be multiplied separately according to the distributive property.
If we have $(x - 2) \times 3$, the task is to apply multiplication to both $x$ and $-2$. This involves a step where the multiplier, here the number 3,

multiplies the variable term: $3 \times x = 3x$
multiplies the constant term: $3 \times -2 = -6$

Once these individual multiplications are performed, they're grouped back together.

Simplifying Expressions

Simplifying expressions is all about making them as concise as possible, usually by combining like terms and completing the necessary arithmetic operations. It's a way of rewriting an expression in its simplest form without changing its value.
In our example, after distributing the 3 through the expression $(x - 2)$, you're left with $3x - 6$. This result is considered simplified because all multiplication has been executed and there are no similar terms left to combine. Understanding when an expression is truly simplified helps in solving algebraic equations efficiently.

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91影视

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

Short Answer

Step by step solution

Understand the Problem

Distribute the 3

Calculate Each Multiplication

Combine the Results

Key Concepts

Algebraic Expressions

Multiplication in Algebra

Simplifying Expressions

One App. One Place for Learning.

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