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Combining ("Gathering") Like Terms with Exponents

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Combining ("Gathering") Like Terms with Exponents

Study Guide

Key Definition

The terms of a mathematical expression that are separated by a plus (+) or minus (–) sign are called like terms if their variable parts and their exponents on each corresponding variable are identical. Like terms can be combined by adding or subtracting their coefficients.

Important Notes

Like terms are gathered by adding or subtracting their coefficients.
The variable part and exponents stay the same; we just add the coefficients (the numerical portion of the terms).
Unlike terms cannot be added or subtracted.

Mathematical Notation

$x^n$ means x raised to the power of n

Remember to use proper notation when solving problems

Why It Works

Like terms share identical variable parts and exponents, so when we add or subtract their coefficients we remain within the same class of terms by the closure property of addition. This simplifies the expression while preserving its value.

Remember

Always keep the variable part the same when combining like terms.

Quick Reference

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

Understanding Combining ("Gathering") Like Terms with Exponents

Choose your learning level

Beginner

Start here! Easy to understand

Beginner Explanation

Simple explanation with the example $2x^2 + 3x^2 = 5x^2$

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Combine the like terms in the expression $3x^2 + 2x^2$

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If a teenager receives 3x dollars from his mother and 2x dollars from his father, what is the total money received?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Combine the like terms in the expression $5y^3 - 3y^3 + 2y$

Challenge Quiz

Single Choice Quiz

Advanced

Combine the like terms in the expression $6x^2 + 5x + 4 - 4x^2 + 7x - 8$

Recap

Watch & Learn

Review key concepts and takeaways