Problem preview
A-APR.1 Warmup M3-001-A07-V01

Add, subtract, and multiply polynomials beyond quadratic cases.

Multiply a binomial and a trinomial with a box or area model

Problem

Use the box model to expand and simplify \((x~+~3)(x^2~+~2x~+~5)\).

Big Picture

What this problem is really about

The box model organizes the multiplication so every row label meets every column label exactly once. We’ll fill all six cells with those term products, then collect cells that have the same power of x. Because the grid accounts for every pairing, combining its like terms gives the complete expansion.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
A-APR.1
Category
Algebra
Domain
Arithmetic with Polynomials and Rational Expressions
Objective
Add, subtract, and multiply polynomials beyond quadratic cases.
Problem type
Multiply a binomial and a trinomial with a box or area model