Simplifying Expressions

Combining Like Terms

An algebraic expression consisting of two or more like terms can be simplified by combining like terms.

Like terms are terms that have the same variable the same variable raised to the same exponent. They only differ in their coefficients.

The following diagram shows some examples of like terms. Scroll down the page for more examples and solutions on simplifying expressions by combining like terms.

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Like Terms
Like terms are terms that have the same variable(s) raised to the same power(s). The coefficients (the numbers in front of the variables) can be different.

Examples of Like Terms:
3x, -5x, 0.2x, and x (all have the variable ‘x’ raised to the power of 1)
2y², 7y², and -y² (all have the variable ‘y’ raised to the power of 2)
4ab, -9ab, and 1/2 ab (all have the variables ‘a’ and ‘b’ each raised to the power of 1)
5, -12, and 3.7 (these are constant terms, and all constants are like terms)

Why are like terms important?
Like terms can be combined by adding or subtracting their coefficients. This is a fundamental step in simplifying algebraic expressions and solving equations.

Unlike Terms
Unlike terms are terms that have different variables or the same variables raised to different powers.

Examples of Unlike Terms:
3x and 3y (different variables)
2x² and 5x (same variable, different exponents)
4ab and 4a²b (same variables, but the power of ‘a’ is different)
2 and 2x (one is a constant, the other has a variable)
xy and x (different combinations of variables)
a²b and ab² (same variables, but the powers are switched)

Unlike terms cannot be directly combined through addition or subtraction. They remain separate in the algebraic expression.

Understanding the difference between like and unlike terms is crucial for correctly simplifying algebraic expressions and solving equations. Always pay close attention to the variables and their powers when identifying like terms.

Example:
Simplify the expressions:
a) 14x + 5x
b) 5y – 13y
c) p – 3p

Solution:
a) 14x + 5x = (14 + 5)x = 19x
b) 5y – 13y = (5 –13)y = –8y
c) p – 3p = (1 – 3)p = – 2p

To simplify an algebraic expression that consists of both like and unlike terms, it might be helpful to first move the like terms together. (When moving the terms, we must remember to move the + or – attached in front of them).

Example:
Simplify 3x + 2y – 2x + 6

Solution:
3x + 2y – 2x + 6
= 3x– 2x + 2y + 6
= (3 – 2)x + 2y + 6
= x + 2y + 6

Example:
Simplify 3x + 2a – 4x

Solution:
3x + 2a – 4x
= 3x – 4x + 2a
= (3 – 4)x + 2a
= –x + 2a

The following videos show some examples of simplifying expressions by combining like terms.

Example:
Simplify -7ab + 6b - 3ab - 4b - 3ab

• Show Video Lesson

Example:
Simplify 7xy + 9yz - 3xy - 3yz + 7xy - 2yz

• Show Video Lesson

Simplify Algebraic Expressions - Combine Like Terms

Examples:

1. 4x³ - 2x² + 5x³ + 2x - 4x² - 6x
2. 4y - 2x + 5 - 6y + 7x - 9

• Show Video Lesson

Simplify an Algebraic Expression by Combining Like Terms.

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

Example:
Simplify
a) 4x³ + x² - 2x³ + 5
b) 10x⁵ + 3(2x⁵ - 4b²)

• Show Video Lesson

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