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Difference of Squares

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Difference of Squares

Study Guide

Key Definition

The difference of squares formula is $a^2 - b^2 = (a + b)(a - b)$, used to factorize expressions.

Important Notes

The formula $a^2 - b^2 = (a + b)(a - b)$ is specific to two squared terms.
The terms $a$ and $b$ are the square roots of the original squares.
This method simplifies complex polynomials.
Useful in solving quadratic equations.
Commonly used in algebraic manipulations.

Mathematical Notation

$-$ represents subtraction

$(a + b)$ and $(a - b)$ are binomials

$a^2$ and $b^2$ are perfect squares

Use correct binomial notation and parentheses when applying the difference of squares formula.

Why It Works

By expanding $(a + b)(a - b)$ using FOIL, the middle terms cancel out, resulting in $a^2 - b^2$.

Remember

The key formula is $a^2 - b^2 = (a + b)(a - b)$.

Quick Reference

Difference of Squares:$a^2 - b^2 = (a + b)(a - b)$

Understanding Difference of Squares

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Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

When you see $a^2 - b^2$, you can factor it as $(a + b)(a - b)$. For example, $9^2 - 4^2 = (9 + 4)(9 - 4) = 65$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the result of $9^2 - 4^2$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A square garden with side $15$ meters and a smaller square section of $10$ meters is removed. What is the remaining area?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Express $49 - 36$ as a difference of squares.

Challenge Quiz

Single Choice Quiz

Advanced

Solve $x^2 - 25 = 0$ using difference of squares.

Recap

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Review key concepts and takeaways