Expanding Parentheses

Article Contents

1. The Distributive Law
2. One Term Outside Parentheses
3. Multiplying Binomials (FOIL)
4. Multiple Terms Outside
5. Common Mistakes
6. Practice Examples
7. Interactive Exercises

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1. The Distributive Law {#the-distributive-law}

The distributive law states that multiplication can be "distributed" over addition or subtraction:

Visual Explanation

You have $3$ groups of $(4+2)$:

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2. One Term Outside Parentheses {#one-term-outside}

Basic Example

Negative Sign

Decimal Numbers

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3. Multiplying Binomials (FOIL) {#multiplying-binomials}

When multiplying two binomials, use the FOIL method:

Result

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4. Multiple Terms Outside {#multiple-terms-outside}

Two Terms

1. $2x\cdot x=2x^2$
2. $2x\cdot (-4)=-8x$
3. $3\cdot x=3x$
4. $3\cdot (-4)=-12$

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5. Common Mistakes {#common-mistakes}

❌ Mistake 1: Forgetting the Sign

The minus sign in front of parentheses changes ALL signs inside!

❌ Mistake 2: Incorrect Expansion

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6. Practice Examples {#practice-examples}

Example 1: Simple Expansion

Example 2: Two Parentheses

Example 3: With Zero

This is the difference of squares formula!

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7. Interactive Exercises {#interactive-exercises}

Practice expanding:

• Expanding Expressions
• Multiplying Polynomials
• Difference of Squares

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Formula Summary

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Related Articles

• Introduction to Algebra – basic concepts
• Factoring – reverse process
• Difference of Squares – useful formula