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Binomial Expansion Introduction
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Binomial Expansion Introduction
📚 Part 1: Understanding Area Models
1. Look at the area model for (a + b)². Which expression represents the total area?
a² + b²
a² + 2ab + b²
(a + b) × 2
a + b + 2
2. In the area model for (x + 3)², what are the dimensions of each rectangle? (Check all that apply)
x by x
x by 3
3 by 3
x by 6
3. When we expand (m + 4)², the middle term 2ab becomes:
4m
8m
2m
m + 4
4. Complete the expansion: (p + 5)² = p² + _______ + 25
✏️ Part 2: Drawing and Expanding
5. Draw an area model for (x + 2)² in the space below. Label each section with its area.
6. Using your area model from Question 5, write the complete algebraic expansion:
(x + 2)² = _________________
7. Expand the following binomials using the pattern a² + 2ab + b²:
a) (y + 6)² = _________________
b) (3 + t)² = _________________
c) (s + 1)² = _________________
8. Explain in your own words how the area model helps you understand binomial expansion:
🚀 Part 3: Challenge Questions
9. Extension: If the total area of a square is represented by (n + 7)², and you know one small square has area n², what is the combined area of the two rectangular sections?
10. Reflection: How would you explain to a friend why (a + b)² ≠ a² + b²? Use an example to support your explanation.
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