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Chapter 4: Problem 102

How do you add like terms?

Short Answer

Expert verified
Adding like terms involves combining the coefficients of the terms, leading to a simplified expression. For instance, '2x' and '5x' add up to give '7x'.

Step by step solution

01

Understand Like Terms

First, it's important to identify what 'like terms' are. For instance, '2x' and '5x' are like terms because both terms have the same variable 'x'. The numbers '2' and '5' are called coefficients.
02

Combine the coefficients

When you are adding like terms, you add the coefficients together while keeping the variable part the same. So, in the example of '2x' and '5x', you would add the coefficients '2' and '5' together. That would give '7x'.
03

Simplified expression

The result of the addition is the simplified expression. Here '7x' is the final simplified expression, which is the sum of two like terms '2x' and '5x'.

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Key Concepts

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

Coefficients
Coefficients play a crucial role in understanding algebraic expressions and equations. They are the numerical part of terms that help us understand how many of a particular variable exist in the term. In the expression \(2x\), the '2' is the coefficient, indicating that there are two 'x's. Similarly, in \(5x\), the '5' is the coefficient, showing five 'x's present.

When adding or subtracting like terms, it's essential to combine their coefficients correctly. Coefficients tell us how to scale the variables within the expression. They are always multiplied by the variable they accompany and remain consistent when performing arithmetic operations with like terms.
Simplified Expression
A simplified expression is an expression where all like terms have been combined and unnecessary terms have been eliminated. By simplifying, we make complex algebraic expressions easier to work with.

Let's consider our running example: when combining \(2x\) and \(5x\), you end up with the simplified expression \(7x\). The simplification process involves adding the coefficients of like terms while keeping the variables unchanged. This results in a more streamlined and manageable expression to work with in further calculations. This process helps to clear up an otherwise cluttered equation and prepare it for future operations or analysis.
Combining Terms
Combining terms is the process of adding or subtracting terms that share the same variables and exponents, known as like terms. Understanding how to combine these terms is foundational in algebra because it allows for the simplification of expressions and solving of equations.

When terms are combined, only the coefficients are added or subtracted, while the variable component remains unchanged. For instance, combining \(2x\) and \(5x\) results in \(7x\), as the variables are the same and form the like terms. This essential technique streamlines algebraic operations and aids in developing a more comprehensive understanding of mathematical expressions.

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Most popular questions from this chapter

How do you recognize like terms?

Perform the operations. $$\left(4 c^{2}+3 c-2\right)+\left(3 c^{2}+4 c+2\right)$$

Simplify or solve as appropriate. $$(x-3)^{2}-(x+3)^{2}$$

How would you check the results of a division?

Perform the operations. $$\begin{aligned}&(3 x)^{2}-4 x^{2}+10 x^{2}\\\\\end{aligned}$$
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