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Overview
Plus (+) Standards
19. NY.A-APR.C.5+
19.2 Binomial theorem
The Binomial Theorem
Expand (x+y) to any power using the coefficients from row n of Pascal's triangle.
What You'll Learn
(x+y)^n expands using coefficients that match row n of Pascal's triangle.
Each coefficient is C(n,k), the same value counted by combinations.
In each term, the power of x decreases while the power of y increases.
(x+y)^3 = x^3 + 3x^2y + 3xy^2 + y^3, using row 3: 1, 3, 3, 1.
For (x-y)^n or a coefficient like 2x, substitute the full term including its sign.
What You'll Practice
1
Expanding binomials with positive and negative terms to various powers
2
Finding specific terms (fourth term, middle term, constant term) in expansions
3
Calculating coefficients for terms containing specific variable powers
4
Working with binomials containing fractions and multiple variables
Why This Matters
The Binomial Theorem saves you enormous time when expanding expressions raised to high powers. Instead of multiplying out (x + 2)^10 by hand, you'll use this efficient formula throughout algebra, calculus, probability, and statistics.
Before You Start — Make Sure You Can:
This Unit Includes
7 Video lessons
Practice exercises
Learning resources
Skills
Binomial Theorem
Combinatorics
Polynomial Expansion
Coefficients
Exponents
Pascal's Triangle
Algebra
NY Curriculum Aligned