Problem preview
A-APR.5 Warmup M3-005-A07-V01

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

Fill in a missing coefficient in a binomial expansion

Problem

Complete \((x~+~y)^5~=~x^5~+~5x^4y~+~\text{\_\_}x^3y^2~+~...\) .

Big Picture

What this problem is really about

Locate the blank by matching its exponent pair to a position in the expansion. The second variable’s exponent gives the zero-based index k, and the corresponding entry in Pascal’s row—or the equivalent combination—supplies the coefficient. Check that the first variable’s exponent is n minus k so an adjacent row entry is not used accidentally.

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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
Fill in a missing coefficient in a binomial expansion