Distribute and Conquer Notes Handout
Pre-Algebra & Algebra 1 Guided Notes & Practice
Distribute and Conquer
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Part 1: Key Concepts & Core Rule (Fill In The Blanks)
1. In everyday life, to distribute means to or share equally among all members of a group.
2. The Distributive Property states that multiplying an outside factor by a sum or difference means that outside factor by each term inside individually.
Algebraic Rule
\(a(b + c) = \) \(+\)
\(a(b - c) = \) \(-\)
Visual Reminder: The Rainbow Method
Draw multiplying arcs from the outside factor to every term inside! Always watch your (+ or -).
Part 2: Guided Model Walkthrough
Model 1 Standard
\(3(2x + 7)\)
\(= 3 \cdot 2x + 3 \cdot 7\)
\(= 6x + 21\)
Model 2 Sign Trap
\(-4(3x - 5)\)
\(= (-4)(3x) - (-4)(5)\)
\(= -12x + 20\)
Model 3 Invisible -1
\(-(5w - 8)\)
\(= -1(5w) - (-1)(8)\)
\(= -5w + 8\)
Part 3: Independent Practice
Show multiplication steps clearly in the workspace
1. Simplify: \(5(3x + 8)\)
Final Answer:
2. Simplify: \(-6(2m - 7)\)
Final Answer:
3. Simplify: \(7(4 - 3y)\)
Final Answer:
4. Simplify: \(-(9k + 14)\)
Final Answer:
Distributive Property Guided Notes • Section 1 Page 1 of 2
Advanced Skill Multi-Step Expressions
Distribute & Combine Like Terms (DP & CLT)
Order of Operations 1. DP → 2. CLT
The Two-Step Strategy (Fill In The Blanks)
1 Step 1: Distribute First!
Clear parentheses by multiplying the outside factor by terms the grouping symbols. Do NOT distribute to terms outside!
2 Step 2: Combine Like Terms!
Identify terms with the exact same and exponent. Add or subtract their .
Master Model: \(4(2x + 3) + 5x - 7\) Step-by-Step Breakdown
1. Distribute 4 \(8x + 12 + 5x - 7\)
2. Group Like Terms \((8x + 5x) + (12 - 7)\)
3. Final Simplified Form \(13x + 5\)
DP + CLT Work Space
Show step 1 (DP) and step 2 (CLT) for each problem
5. Simplify: \(3(4x + 2) + 6x\)
Final Answer:
6. Watch The Sign: \(9y - 4(2y - 5)\)
Final Answer:
7. Double Distribution: \(2(3a + 4) + 5(2a - 1)\)
Final Answer:
8. Challenge: \(15 - 3(2m - 4) + 8m\)
Final Answer:
Trap Spotter: Analyze the Error
Jordan's Incorrect Work:
\(7 - 2(3x + 5)\)
\(= 5(3x + 5)\)
\(= 15x + 25\) ✗
What was Jordan's mistake?
Correct Answer:
Distributive Property & CLT Guided Notes • Section 2 Page 2 of 2
