In these lessons, we will learn how to simplify expressions by adding or subtracting like terms (combining like terms).

Related Topics: More Algebra Lessons

### Simplifying Expressions Of Like Terms

*x* + 5*x *

b) 5*y* – 13*y *

c)*p* – 3*p *

d)

*x* + 5*x* = (14 + 5)*x* = 19*x*

b) 5*y* – 13*y* = (5 –13)*y* = –8*y*

c)*p* – 3*p* = (1 – 3)*p* = – 2*p *

d)

### Simplifying Expressions Of Like and Unlike Terms

**How to identify like terms and combine like terms?**

Two or more like terms are like terms if they have the same variable (or variables) with the same exponent.

To combine like terms, we add or subtract the coefficients. The variable factors remain the same.

Examples:

Which of these terms are like terms?

-2x^{3}, -2x, 2y, 7x^{3}, 4y, 6x^{2}, y^{2}

Simplify each polynomial, if possible.

4x^{3} - 7x^{3}

2y^{2} + 4y - y^{2} + 2 - 9y - 5 + 2y
**Identify and Combine Like Terms**

Examples:

3v + 7v - v + v

5x + 6x^{2} + 8x + x^{3} - x^{2}

5c + 2d + c - (-3)d

1/2 y - 3/7 y + y

**Examples of combining like terms**

Examples:

1. 8x + 5y - 17x

2. 7x - 8 - 11x

3. 3a + 5c - 9a + 2a -c

4. 3xy + 4xy + 5x^{2}y + 6xy^{2}

5. 5y^{2}x - 2x^{2}y + 8y^{2}x + 2xy - x^{2}y + 3xy

6. 11a + 30a -18a

**Simplify an Algebraic Expression by Combining Like Terms**

This video shows how to simplify algebraic expressions by combining like terms by adding, subtracting, and using distribution.

Examples:

1. 4x^{3} + x^{2} - 2x^{3} + 5

2. 10x^{5} + 3(2x^{5} - 4b^{2})

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Related Topics: More Algebra Lessons

An algebraic expression consisting of like terms can be simplified by adding or subtracting the coefficients of the like terms.

* Example*

Simplifying the expressions:

a) 14b) 5

c)

d)

* Solution:*

b) 5

c)

d)

To simplify an algebraic expression that consists of both like and unlike terms, we need to

** Step 1:** move the like terms together

**Step 2:** add or subtract their coefficients.

When moving the terms, we must remember to move the + or – attached in front of them. For example,

* Example: *

Simplify 3*x* + 2*a* – 4*x*

* Solution: *

3*x * + 2*a * – 4*x
*= 3

* Example: *

Simplify *b* + 1.4*c* - 0.6*b* + 2

* Solution: *

* b* + 1.4*c* - 0.6*b* + 2

= *b* + 1.4*c* - 0.6*b* + 2

*= b* – 0.6*b* + 1.4*c* + 2

*= * 0.4* b* + 1.4* c* + 2

Two or more like terms are like terms if they have the same variable (or variables) with the same exponent.

To combine like terms, we add or subtract the coefficients. The variable factors remain the same.

Examples:

Which of these terms are like terms?

-2x

Simplify each polynomial, if possible.

4x

2y

Examples:

3v + 7v - v + v

5x + 6x

5c + 2d + c - (-3)d

1/2 y - 3/7 y + y

Examples:

1. 8x + 5y - 17x

2. 7x - 8 - 11x

3. 3a + 5c - 9a + 2a -c

4. 3xy + 4xy + 5x

5. 5y

6. 11a + 30a -18a

This video shows how to simplify algebraic expressions by combining like terms by adding, subtracting, and using distribution.

Examples:

1. 4x

2. 10x

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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