Simplifying Algebraic Expressions: Combining Like Terms

Understanding Algebraic Expressions

Ever wonder how mathematicians organize complex equations? It all starts with knowing the parts of an algebraic expression. An algebraic expression consists of different types of terms that we can identify and manipulate.

Let's break down the important vocabulary:

• A term is a number, variable, or combination of both through multiplication or division
• A constant is a term with no variable (just a number by itself)
• A coefficient is the number in front of a variable
• A variable is a letter that represents an unknown value
• Like terms have identical variable parts with the same exponents

Quick Tip: Think of like terms as "same species" in the algebra world - they have the identical variable patterns, just different coefficients!

When you see something like 6a² - 5ab + 3b - 12, you can now identify each part. This skill will be essential for simplifying expressions in the next steps.

Simplifying by Combining Like Terms

Looking at an expression like 6a² - 5ab + 3b - 12, we can identify that:

• The terms are: 6a², -5ab, 3b, and -12
• The only constant is -12
• The coefficients are: 6, -5, 3

To determine if terms are like terms, we need to compare their variable factors. For example, 7a and -3a are like terms because they have the same variable $a$. However, 6ab and -2a are not like terms because their variable factors differ.

Simplifying expressions follows three easy steps:

1. Identify the like terms
2. Group the like terms together
3. Combine the coefficients (add or subtract)

For example, with 7m + 3m + 6n - 5n - 2m:

• Group like terms: $7m + 3m - 2m$ + $6n - 5n$
• Combine coefficients: (8m) + $n$
• Final answer: 8m + n

Remember: You can only combine the coefficients of like terms - never try to combine terms with different variables!