Rewriting the Expression with Combined Terms

Oct 13, 2025 by miodeya.com 52 views

Introduction

In algebra, combining like terms is a fundamental concept that helps simplify complex expressions. It involves adding or subtracting terms that have the same variable and exponent. In this article, we will focus on rewriting each expression by combining like terms, using the given expression as an example.

Understanding Like Terms

Like terms are terms that have the same variable and exponent. For example, 2x and 4x are like terms because they both have the variable x and the same exponent (1). On the other hand, 2x and 3y are not like terms because they have different variables (x and y).

Rewriting the Expression

Let's rewrite the given expression by combining like terms:

${$ (0.4x + 0.9) + (0.5x - 0.7) + (1.6x - 7.5)$}$

To combine like terms, we need to identify the terms that have the same variable and exponent. In this expression, we have three terms with the variable x: 0.4x, 0.5x, and 1.6x. We also have two constant terms: 0.9 and -0.7, and another constant term -7.5.

Step 1: Combine the x Terms

First, let's combine the x terms:

${ $0.4x + 0.5x + 1.6x\$}$

To combine these terms, we need to add their coefficients (the numbers in front of the variable). The coefficients are 0.4, 0.5, and 1.6. Adding these coefficients, we get:

${ $0.4 + 0.5 + 1.6 = 2.5\$}$

So, the combined x term is 2.5x.

Step 2: Combine the Constant Terms

Next, let's combine the constant terms:

${ $0.9 - 0.7 - 7.5\$}$

To combine these terms, we need to add or subtract their values. First, let's subtract 0.7 from 0.9:

${ $0.9 - 0.7 = 0.2\$}$

Then, let's subtract 7.5 from 0.2:

${ $0.2 - 7.5 = -7.3\$}$

So, the combined constant term is -7.3.

Rewriting the Expression with Combined Terms

Now that we have combined the x terms and the constant terms, we can rewrite the expression:

${ $2.5x - 7.3\$}$

Conclusion

In this article, we learned how to rewrite an expression by combining like terms. We identified the like terms in the given expression and combined their coefficients and values. The resulting expression is simpler and easier to work with. By combining like terms, we can simplify complex expressions and make them more manageable.

Examples of Combining Like Terms

Here are some examples of combining like terms:

${ $2x + 3x + 4x\$}$ becomes ${ $9x\$}$
${ $5y - 2y + 3y\$}$ becomes ${ $6y\$}$
${ $2x + 5y - 3x + 2y\$}$ becomes ${$ -x + 7y$}$

Tips for Combining Like Terms

Here are some tips for combining like terms:

Identify the like terms in the expression.
Combine the coefficients of the like terms.
Combine the values of the like terms.
Simplify the resulting expression.

Common Mistakes to Avoid

Here are some common mistakes to avoid when combining like terms:

Not identifying the like terms in the expression.
Not combining the coefficients of the like terms.
Not combining the values of the like terms.
Not simplifying the resulting expression.

Conclusion

Introduction

Combining like terms is a fundamental concept in algebra that helps simplify complex expressions. In our previous article, we learned how to rewrite an expression by combining like terms. In this article, we will provide a Q&A guide to help you understand and apply the concept of combining like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, 2x and 4x are like terms because they both have the variable x and the same exponent (1).

Q: How do I identify like terms in an expression?

A: To identify like terms in an expression, look for terms that have the same variable and exponent. For example, in the expression 2x + 3x + 4x, the terms 2x, 3x, and 4x are like terms because they all have the variable x and the same exponent (1).

Q: How do I combine like terms?

A: To combine like terms, add or subtract their coefficients (the numbers in front of the variable). For example, in the expression 2x + 3x + 4x, the coefficients are 2, 3, and 4. Adding these coefficients, we get:

${ $2 + 3 + 4 = 9\$}$

So, the combined term is 9x.

Q: What if I have a negative coefficient?

A: If you have a negative coefficient, simply add or subtract it from the other coefficients. For example, in the expression -2x + 3x + 4x, the coefficients are -2, 3, and 4. Adding these coefficients, we get:

${$ -2 + 3 + 4 = 5$}$

So, the combined term is 5x.

Q: Can I combine terms with different variables?

A: No, you cannot combine terms with different variables. For example, in the expression 2x + 3y, you cannot combine the terms 2x and 3y because they have different variables (x and y).

Q: What if I have a term with a variable and a constant?

A: If you have a term with a variable and a constant, you can combine it with other terms that have the same variable and exponent. For example, in the expression 2x + 3 + 4x, you can combine the terms 2x and 4x to get:

${ $2x + 4x = 6x\$}$

Then, you can combine the constant term 3 with the combined term 6x to get:

${ $6x + 3\$}$

Q: Can I simplify an expression by combining like terms?

A: Yes, you can simplify an expression by combining like terms. By combining like terms, you can rewrite the expression in a simpler form that is easier to work with.

Q: What are some common mistakes to avoid when combining like terms?

A: Some common mistakes to avoid when combining like terms include:

Not identifying the like terms in the expression.
Not combining the coefficients of the like terms.
Not combining the values of the like terms.
Not simplifying the resulting expression.

Conclusion

Combining like terms is an essential concept in algebra that helps simplify complex expressions. By identifying the like terms in an expression and combining their coefficients and values, we can rewrite the expression in a simpler form. In this article, we provided a Q&A guide to help you understand and apply the concept of combining like terms.