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A-APR.5 Warmup M3-005-A01-V01

Apply the Binomial Theorem for expanding (x+y)^n using Pascal's Triangle or combinatorial reasoning.

Expand a binomial power using Pascal's Triangle

Problem

Use Pascal's Triangle to expand \((x~+~y)^4\).

Pascal's Triangle through row 4, with row 4 highlighted as 1, 4, 6, 4, 1 for (x+y)^4. Apply these coefficients to descending powers of x and ascending powers of y; the expansion is withheld. Open full size
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What this problem is really about

A binomial expansion combines two synchronized patterns. Pascal’s row matching the outside exponent supplies the coefficients, while the first variable’s exponent steps down and the second variable’s exponent steps up. Pair each coefficient with one complementary exponent pair, checking that the exponents in every term add to the original power.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
A-APR.5
Category
Algebra
Domain
Arithmetic with Polynomials and Rational Expressions
Objective
Apply the Binomial Theorem for expanding (x+y)^n using Pascal's Triangle or combinatorial reasoning.
Problem type
Expand a binomial power using Pascal's Triangle