Pascal's Triangle Worksheet
Explore the patterns and properties of Pascal's Triangle, including its construction, binomial coefficients, and relationships to other mathematical concepts.
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Pascal's Triangle Exploration
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Read each question carefully and answer to the best of your ability. Show all your work where applicable.
1. Pascal's Triangle starts with a single number at the top, which is considered row 0.
2. Each number in Pascal's Triangle is the of the two numbers directly above it.
3. The numbers along the edges of Pascal's Triangle are always .
4. Complete the 5th row of Pascal's Triangle (Row 0 is 1):
Row 0: 1
Row 1: 1 1
Row 2: 1 2 1
Row 3: 1 3 3 1
Row 4: 1 4 6 4 1
Row 5: __ __ __ __ __ __
5. What is the sum of the numbers in the 4th row of Pascal's Triangle (starting with Row 0)?
8
16
32
64
6. The numbers in each row of Pascal's Triangle are symmetric.
True
False
7. Use Pascal's Triangle to expand the binomial expression (x + y)³.
8. What is the coefficient of the x²y³ term in the expansion of (x + y)⁵?