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Combining ("Gathering") Like Terms

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Combining ("Gathering") Like Terms

Study Guide

Key Definition

Terms of an expression are the parts separated by $+$ or $-$. Like terms have the same variable part.

Important Notes

Like terms share identical variable parts.
Combine like terms by adding or subtracting their coefficients.
Rearrange terms using $\text{Commutative}$ and $\text{Associative Properties}$.
Add or subtract coefficients of like terms.
Unlike terms cannot be directly combined.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

Combining like terms simplifies expressions by reducing the number of terms while maintaining equality.

Remember

Always check for like terms by examining variable parts.

Quick Reference

Distributive Property:$a(b+c) = ab + ac$

Understanding Combining ("Gathering") Like Terms

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Combine like terms by adding or subtracting their coefficients when they have the same variable parts. For example, $3x + 2x = (3 + 2)x = 5x$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Simplify $6x + 4y - 2x + 2$.

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $3a + 5b$ candies. Your friend gives you $2a - 3b$ candies. How many candies do you have now?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Simplify the expression $12a + 3b - 8b - 8a + a - 7b$.

Challenge Quiz

Single Choice Quiz

Advanced

Simplify $4x + 18y - 3x - 7x + 3xy$.

Recap

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Review key concepts and takeaways