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Binomial Expansion Area Models
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Binomial Expansion Area Models
📚 Part 1: Understanding Area Models
1. Look at the area model for (a+b)². What are the four regions that make up the complete square?
a², ab, ab, b²
a², 2ab, b²
a², b², ab, ba
a, b, a, b
2. When we expand (x+3)², which expression is correct?
x² + 6x + 9
x² + 3x + 9
x² + 9
x² + 6x + 6
3. In the area model for (a+b)², how many rectangles have area 'ab'?
1
2
3
4
4. Which parts of the area model represent squared terms? (Select all that apply)
The top-left corner (a²)
The bottom-right corner (b²)
The top-right rectangle (ab)
The bottom-left rectangle (ab)
✏️ Part 2: Drawing and Expanding
5. Draw an area model for (x+2)² in the box below. Label each region with its area.
6. Using your area model from question 5, write the complete expansion of (x+2)²:
(x+2)² = _____ + _____ + _____
7. Complete this expansion using the area model method: (y+5)²
8. Explain in your own words why (a+b)² equals a² + 2ab + b² and not a² + b²:
🎯 Part 3: Challenge Questions
9. If the total area of a square is (m+4)² and one corner square has area 16, what is the value of one side of that corner square?
10. Extension: Can you predict what (a+b+c)² might look like using area models? Describe what you think the expansion would contain:
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