Examples of Combining Like Terms

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Introduction

When we add two polynomials together, we are combining like terms, or terms with the same power. This is similar to combining like terms in linear expressions. In this article, we will explore how to combine like terms in polynomials and provide examples to illustrate the concept.

What are Like Terms?

Like terms are terms that have the same variable and exponent. For example, in the polynomial 2x^2 + 3x^2, the terms 2x^2 and 3x^2 are like terms because they both have the variable x and the exponent 2.

How to Combine Like Terms

To combine like terms, we add or subtract the coefficients of the like terms. The coefficients are the numbers that multiply the variables. For example, in the polynomial 2x^2 + 3x^2, the coefficients are 2 and 3. We add these coefficients to get 5x^2.

Examples of Combining Like Terms

Example 1

Combine the following polynomials: 2x^2 + 3x^2 + 4x^2

To combine like terms, we add the coefficients of the like terms:

2x^2 + 3x^2 + 4x^2 = (2 + 3 + 4)x^2 = 9x^2

Example 2

Combine the following polynomials: 2x^2 + 3x^2 - 4x^2

To combine like terms, we add the coefficients of the like terms:

2x^2 + 3x^2 - 4x^2 = (2 + 3 - 4)x^2 = x^2

Example 3

Combine the following polynomials: 2x^2 + 3x^2 + 4x + 5x

To combine like terms, we add the coefficients of the like terms:

2x^2 + 3x^2 + 4x + 5x = (2 + 3)x^2 + (4 + 5)x = 5x^2 + 9x

Tips for Combining Like Terms

Make sure to identify the like terms in the polynomial.
Add or subtract the coefficients of the like terms.
Simplify the expression by combining the like terms.

Conclusion

Combining like terms in polynomials is an important concept in algebra. By following the steps outlined in this article, you can combine like terms and simplify expressions. Remember to identify the like terms, add or subtract the coefficients, and simplify the expression.

Exercise #4

Write each of the following sums in standard form by combining like terms.

2x^2 + 3x^2 + 4x^2
2x^2 + 3x^2 - 4x^2
2x^2 + 3x^2 + 4x + 5x
2x^2 + 3x^2 + 4x^2 + 5x
2x^2 + 3x^2 - 4x^2 - 5x^2

Answer Key

9x^2
x^2
5x^2 + 9x
5x^2 + 9x
-7x^2
Combining Like Terms in Polynomials: Q&A =============================================

Introduction

Combining like terms in polynomials is an important concept in algebra. In our previous article, we explored how to combine like terms and provided examples to illustrate the concept. In this article, we will answer some frequently asked questions about combining like terms in polynomials.

Q&A

Q: What are like terms in polynomials?

A: Like terms are terms that have the same variable and exponent. For example, in the polynomial 2x^2 + 3x^2, the terms 2x^2 and 3x^2 are like terms because they both have the variable x and the exponent 2.

Q: How do I combine like terms in polynomials?

A: To combine like terms, you add or subtract the coefficients of the like terms. The coefficients are the numbers that multiply the variables. For example, in the polynomial 2x^2 + 3x^2, the coefficients are 2 and 3. You add these coefficients to get 5x^2.

Q: What if I have a polynomial with multiple like terms?

A: If you have a polynomial with multiple like terms, you can combine them by adding or subtracting the coefficients. For example, in the polynomial 2x^2 + 3x^2 + 4x^2, you can combine the like terms by adding the coefficients: (2 + 3 + 4)x^2 = 9x^2.

Q: Can I combine like terms with different variables?

A: No, you cannot combine like terms with different variables. For example, in the polynomial 2x^2 + 3y^2, you cannot combine the like terms because x and y are different variables.

Q: What if I have a polynomial with a negative coefficient?

A: If you have a polynomial with a negative coefficient, you can still combine like terms by adding or subtracting the coefficients. For example, in the polynomial 2x^2 - 3x^2, you can combine the like terms by subtracting the coefficients: (2 - 3)x^2 = -x^2.

Q: Can I combine like terms with different exponents?

A: No, you cannot combine like terms with different exponents. For example, in the polynomial 2x^2 + 3x, you cannot combine the like terms because x^2 and x have different exponents.

Q: How do I know if I have combined like terms correctly?

A: To check if you have combined like terms correctly, you can simplify the expression by combining the like terms. If the expression simplifies to a single term, then you have combined the like terms correctly.

Tips for Combining Like Terms

Make sure to identify the like terms in the polynomial.
Add or subtract the coefficients of the like terms.
Simplify the expression by combining the like terms.
Check your work by simplifying the expression.

Conclusion

Common Mistakes to Avoid

Combining like terms with different variables.
Combining like terms with different exponents.
Not simplifying the expression after combining like terms.
Not checking your work.

Practice Problems

Combine the following polynomials: 2x^2 + 3x^2 + 4x^2
Combine the following polynomials: 2x^2 + 3x^2 - 4x^2
Combine the following polynomials: 2x^2 + 3x^2 + 4x + 5x
Combine the following polynomials: 2x^2 + 3x^2 + 4x^2 + 5x
Combine the following polynomials: 2x^2 + 3x^2 - 4x^2 - 5x^2

Answer Key

9x^2
x^2
5x^2 + 9x
5x^2 + 9x
-7x^2