Distributive Property – Outschool
Distributive Property Lesson
I. The Basics
The distributive property allows you to expand expressions by multiplying each item separately then adding the products.
Example 1: [latex]4(x+7)[/latex]
Multiply the 4 and the x, then the 4 and the 7, then add.
II. Applying Your Knowledge
Example 2: [latex]4(x+7+y) = 4x + 28 + 4y[/latex]
Example 3: [latex]4x^2y^3(24x^3y-5xy+3) = 96x^5y^4 -20x^3y^4+ 12x^2y^3[/latex]
*Remember that when you multiply elements with the same base, you add the exponents.
When there’s a minus sign before parentheses, treat it as a “-1” and distribute:
Example 4: [latex](3x + 7y – 4z) – (4x – 2y + z)[/latex]
→ [latex]3x + 7y – 4z – 4x + 2y – z[/latex] (after you distribute the “-” sign)
→ [latex] -x + 9y – 5z[/latex] (after you combine like terms)
Make sure to multiply each item from one group with each item from the other group:
Example 5: Multiply and simplify [latex](x + 2)(3x + 5)[/latex].
→ [latex]3x^2 + 5x + 6x + 10[/latex]
→ [latex]3x^2 + 11x + 10[/latex]
Don’t be fooled by tricky notation:
Example 6: [latex](6x-7y)^2[/latex]
→ [latex](6x-7y)(6x-7y)[/latex]
→ [latex]36x^2 -42xy -42xy + 49y^2[/latex]
→ [latex]36x^2 – 84xy + 49y^2[/latex]