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Precalculus
18. CC.HSA.APR.C.5
18.1 Pascal's triangle
Pascal's Triangle
Each entry is the sum of the two numbers diagonally above it, and row n gives the binomial-expansion coefficients.
What You'll Learn
Each row starts and ends with 1; each interior entry is the sum of the two above it.
Row 3 is 1, 3, 3, 1 -- the coefficients in the expansion of (x+y) cubed.
The k-th entry in row n equals the combination C(n, k).
You can compute any single entry directly with the combination formula.
Pascal's triangle links counting (combinations) to algebra (binomial expansion).
What You'll Practice
1
Building Pascal's Triangle rows by adding adjacent numbers
2
Expanding binomials like (a+b)^4 and (a+b)^8 using triangle coefficients
3
Converting triangle entries to combination form (nC0, nC1, etc.)
4
Evaluating sums of combinations without a calculator using 2^n formula
Why This Matters
Pascal's Triangle transforms tedious polynomial expansions into simple pattern recognition. You'll use this tool throughout algebra and pre-calculus to expand binomials quickly, understand probability and combinatorics, and see how mathematical patterns connect across topics.
Before You Start — Make Sure You Can:
This Unit Includes
8 Video lessons
Practice exercises
Learning resources
Skills
Binomial Coefficients
Combinations
Pascal's Triangle
Polynomial Expansion
Pattern Recognition
Exponents
Algebra
IL Curriculum Aligned