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The Distributive Property

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The Distributive Property

Study Guide

Key Definition

The distributive property states that for all real numbers $x$, $y$, and $z$, the equation $x(y + z) = xy + xz$ holds true.

Important Notes

You can distribute multiplication over addition: $x(y + z) = xy + xz$
This property is valid for all real numbers.
Helps simplify expressions with parentheses.
Useful in solving equations.
A foundational concept in algebra.

Mathematical Notation

$+$ represents addition

$\times$ or $*$ represents multiplication

$\frac{a}{b}$ represents a fraction

$x^2$ represents x squared

$\sqrt{x}$ represents the square root of x

Remember to use proper notation when solving problems

Why It Works

The distributive property is based on the distributive law, which allows breaking down complex multiplication over addition, making it easier to solve problems. For example, $3(6 + 7) = 3 \times 6 + 3 \times 7$.

Remember

Always apply the distributive property when you see an expression like $a(b + c)$ to simplify your calculations.

Quick Reference

Distributive Property:$x(y + z) = xy + xz$

Understanding The Distributive Property

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The distributive property allows you to multiply a sum by multiplying each addend separately and then add the products: $a(b + c) = ab + ac$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the result of $3(2 + 4)$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you have $5$ packs of stickers. Each pack contains $(10 + 2)$ stickers. How many stickers do you have in total?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

You have a rectangle where the length is $(x + 3)$ and the width is $2$. Use the distributive property to express the area.

Challenge Quiz

Single Choice Quiz

Advanced

Simplify the expression: $4(x + 2y - 3z)$.

Recap

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Review key concepts and takeaways