➕ Algebra 1 · Equations
The Distributive Property cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
The rule
- a(b + c) = ab + ac
- a(b − c) = ab − ac
- Multiply the outside number by EVERY term inside
Signs
- Same signs multiply to a plus
- Different signs multiply to a minus
- −(x + 3) becomes −x − 3 (every sign flips)
Backward (factoring)
- ab + ac = a(b + c)
- Pull out the greatest common factor
- Check by distributing
Example
- 5(2x − 3)
- 5 × 2x = 10x and 5 × (−3) = −15
- = 10x − 15
Watch out
- Do not skip a term
- A term outside the parentheses waits: multiply first
- (x + 3)2 is not x2 + 9
Formulas
- Distributing over addition: a(b + c) = ab + ac
- Distributing over subtraction: a(b − c) = ab − ac
- Parentheses first: (b + c)a = ba + ca
- Factoring (backward): ab + ac = a(b + c)
- Minus sign in front: −(b + c) = −b − c
- Dividing a sum by a number: (b + c) ÷ a = (b ÷ a) + (c ÷ a) (when a ≠ 0)
The Distributive Property cheat sheet from HighSchoolQ.com, for personal study use.