Factoring Using the Distributive Property
A visual walkthrough showing how the distributive property runs in reverse to factor expressions. Starting with 3(2y+5) expanding to 6y+15, the animation reverses the process, highlighting the greatest common factor and grouping terms back inside parentheses. Arrows and color-coded terms make each algebraic transformation visible on screen. Designed for Grade 10 advanced mathematics students learning to recognize GCFs and rewrite expressions as products.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
Create a Grade 10 Advanced Mathematics lesson about **Using the Distributive Property for Factoring**. This is a 3-minute educational mathematics video. Teach the lesson clearly from the beginning, but keep narration concise so there is enough time to SHOW the mathematics. The most important requirement is VISUAL ALGEBRA. The actual equations must be the main visuals. The viewer must SEE the expressions, GCFs, grouping, arrows, and algebraic transformations while the narrator explains them. Do NOT replace algebra with physical objects, blocks, school supplies, people, classroom scenes, stock footage, or decorative illustrations. Use ONLY the mathematics and examples in the detailed plan. Do not introduce other factoring methods. Audience: Grade 10 advanced mathematics student Teaching plan: Create a concise 3-minute VISUAL MATHEMATICS ANIMATION. The narration must be concise, but DO NOT remove the required mathematical steps. The most important thing is that the viewer can SEE the actual algebra being transformed on screen. Use large, clear mathematical notation. Animate equations from one step to the next instead of replacing them with unrelated visuals. ━━━━━━━━━━━━━━━━━━ PART 1 — DISTRIBUTIVE PROPERTY ━━━━━━━━━━━━━━━━━━ Briefly explain that the Distributive Property means multiplying a factor by every term inside parentheses. Show prominently: 3(2y + 5) Animate it into: 3(2y) + 3(5) Then: 6y + 15 Briefly explain that factoring works in the opposite direction. Show: 6y + 15 → 3(2y + 5) State that factoring is the Distributive Property in reverse. ━━━━━━━━━━━━━━━━━━ PART 2 — FACTORING USING THE GCF ━━━━━━━━━━━━━━━━━━ Introduce the idea: First, find the Greatest Common Factor, or GCF. Then use the EXACT example: 12a² + 16a Make this equation large and central. Show: GCF = 4a Then show: 12a² ÷ 4a = 3a 16a ÷ 4a = 4 Animate the expression into: 12a² + 16a → 4a(3a + 4) Clearly show that 4a is outside the parentheses and 3a + 4 is inside. ━━━━━━━━━━━━━━━━━━ PART 3 — CHECK BY DISTRIBUTING ━━━━━━━━━━━━━━━━━━ Briefly check the answer visually. Show: 4a(3a + 4) → 4a · 3a + 4a · 4 → 12a² + 16a Highlight that the result matches the original expression. ━━━━━━━━━━━━━━━━━━ PART 4 — FACTORING BY GROUPING ━━━━━━━━━━━━━━━━━━ Explain briefly that an expression with four terms can be factored by grouping. Use EXACTLY: 2xy + 5x + 8y + 20 Show: (2xy + 5x) + (8y + 20) Then animate the factoring of each group: 2xy + 5x → x(2y + 5) 8y + 20 → 4(2y + 5) Show the complete result: x(2y + 5) + 4(2y + 5) Visually highlight the repeated factor: 2y + 5 Then animate: x(2y + 5) + 4(2y + 5) → (2y + 5)(x + 4) ━━━━━━━━━━━━━━━━━━ PART 5 — QUICK CHECK ━━━━━━━━━━━━━━━━━━ Show: (2y + 5)(x + 4) Then visually distribute: → 2xy + 8y + 5x + 20 Briefly show that this is the same expression as: 2xy + 5x + 8y + 20 ━━━━━━━━━━━━━━━━━━ PART 6 — PRACTICE ━━━━━━━━━━━━━━━━━━ Show the final practice expression: 18x² + 24x Show: GCF =
Make the next one in this series
- Show factoring by grouping for four-term polynomial expressions
- Demonstrate factoring trinomials using the distributive property in reverse
- Compare distributive expansion versus GCF factoring with side-by-side algebra
