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Chapter 10: Problem 145

Multiply. $$4(x+10)$$

Short Answer

Expert verified
4x + 40

Step by step solution

01

Distribute the 4

To multiply the expression, apply the distributive property. Multiply the 4 by each term inside the parentheses. This means you need to multiply 4 by both x and 10 separately: \[4 \times (x + 10)\].
02

Multiply 4 and x

First, multiply 4 by the variable x: \[4 \times x = 4x\].
03

Multiply 4 and 10

Next, multiply 4 by the constant 10: \[4 \times 10 = 40\].
04

Combine the results

Combine the results of your multiplications to form the final expression: \[4x + 40\].

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Key Concepts

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

Multiplying Variables
Multiplying variables is a key component of algebra. When we multiply variables, we follow the rule that variables are combined by multiplication if there is no other operation between them. For example, multiplying a number (constant) by a variable like x results in the expression being multiplied.
In the given exercise, we have the expression \(4(x + 10)\). Here, we need to multiply 4 by each term inside the parentheses.
Let's break it down:
  • The first step is multiplying 4 by x, giving us \(4x\).
  • The second step is multiplying 4 by 10, resulting in 40.
The distributive property allows us to carry out these operations separately before combining their results.
Simplifying Expressions
Simplifying expressions is another fundamental algebra skill. This process involves making an expression as simple as possible. The goal is to write it in the simplest form while keeping the equality valid.
In our exercise, after using the distributive property, we get \(4x + 40\). This is already in a simplified form because:
  • There are no like terms that can be combined.
  • Each part of the expression is already in its simplest form: \(4x\) can't be simplified further, and 40 is a constant.
This highlights the importance of recognizing when an expression is in its simplest form.
Basic Algebra
Basic algebra forms the foundation for higher-level math. In basic algebra, you learn how to work with variables, constants, and simple operations like addition, subtraction, multiplication, and division.
Understanding concepts like the distributive property is crucial. The distributive property states that \(a(b + c) = ab + ac\).
In our exercise, the expression \(4(x + 10)\) can be distributed as follows:
  • We multiply 4 by x to get \(4x\).
  • We then multiply 4 by 10 to get 40.
By understanding and applying these basic rules and properties, problems like these become much simpler to solve and work through.

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Most popular questions from this chapter

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