Chapter 10: The Distributive Property

Adapted from Wentworth's Elementary Algebra for MathDoctor.net

10.1 Spreading the Wealth

The word "distribute" means to give out or deliver. In Algebra, when a number sits right outside a set of parentheses, it is multiplying everything inside those parentheses.

a(b + c) = ab + ac

You can think of the a as a delivery driver. It has to visit every "house" (term) inside the parentheses.

10.2 Walking Through an Example

Let's simplify the expression: 3(x + 4)

Multiply 3 by the first term (x): 3 • x = 3x
Multiply 3 by the second term (4): 3 • 4 = 12
Combine them: 3x + 12

        Common Mistake: Many students forget to multiply the second term. They might write 3x + 4, but that is incorrect! The "driver" must visit both houses.
    

10.3 Handling Negatives

Remember your sign rules from Chapter 6. If the number being distributed is negative, it flips the signs of everything inside.

Example: -2(x - 5)

-2 • x = -2x
-2 • -5 = +10
Result: -2x + 10

10.4 Modern Application: Group Pricing

Imagine you are buying tickets for a group of 5 people. Each person needs a movie ticket (t) and a popcorn (p).

You could write this as: 5(t + p)

Using the distributive property, you know that the total cost is 5 tickets plus 5 popcorns: 5t + 5p.

Chapter 10 Review

Simplify these expressions by distributing:

4(x + 2)
6(y - 3)
-3(a + 4)
x(x + 2)
(Hint: Remember your exponents from Chapter 7!)

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Doctor's Recommendation: Step-by-Step Distribution

The Distributive Property can be overwhelming when an expression is long. Using Post-it Notes to physically cover parts of the problem while you focus on "handing out" the multiplier to each term inside the parentheses is a fantastic way to stay focused and avoid skipping a term.

View Sticky Notes on Amazon

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