Distributive Property in Algebra

The distributive property is a fundamental property in mathematics that connects multiplication with addition and subtraction. It states that multiplying a sum or difference by a number is the same as multiplying each addend or subtrahend individually by the number and then adding or subtracting the products.

The following diagram shows the distributive property formula. Scroll down the page for more examples of the distributive property.
 

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Distributive Property	Evaluate Algebraic Expressions	Evaluate Expressions (Exponents)
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There are two main forms of the distributive property:

1. Distributive Property of Multiplication over Addition:
   The distributive property of addition and multiplication states that multiplying a sum by a number is the same as multiplying each addend by that number and then adding the two products.
   

For any real numbers a, b, and c:
a × (b + c) = (a × b) + (a × c)

This means that if you have a number multiplied by a sum inside parentheses, you can “distribute” the multiplication to each term inside the parentheses and then add the results.
Example:
3(x + 4) = 3 × x + 3 × 4 = 3x + 12

2. Distributive Property of Multiplication over Subtraction: Similarly, if you have a number multiplied by a difference inside parentheses, you can “distribute” the multiplication to each term inside the parentheses and then subtract the results.

For any real numbers a, b, and c:
a × (b - c) = (a × b) - (a × c)

Example:
3(x + 4) = 3 × x - 3 × 4 = 3x - 12

Common Mistakes to Avoid

• Misapplying to division:
  ❌ \( \frac{a+b}{c} \) ≠ \( \frac{a}{c} \) + \( \frac{b}{c} \)
  
• Forgetting to distribute:
  ✓ 3(x+y) = 3x + 3y
  ❌ 3(x + y) ≠ 3x + y
  
• Forgetting to distribute the negative sign:
  ✓ -3(x + y) ≠ -3x - 3y
  ❌-3(x + y) ≠ -3x + 3y
  

Videos
The Distributive Property.
One of the most important and foundational topics in basic mathematics. The concept is explained and example problems are worked out and explained in detail.

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Using the distributive property in algebra.

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Algebra - Distributive Property

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0:00 Definition of the Distributive Property
12:15 Modeling the Distributive Property
18:45 Practice the Distributive Property
28:00 Factor using the Distributive Property

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