Problem preview

A-APR.4 Warmup M3-004-A12-V02

Prove polynomial identities and use them to solve or describe numerical relationships.

Simplify a rational identity while preserving original-domain exclusions

Problem

Simplify \((a^3~-~b^3)/(a~-~b)\) and state the restriction from the original denominator.

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Factor a³-b³ as (a-b)(a²+ab+b²). Cancel a-b to get a²+ab+b², with no restriction.

Factor a³-b³ as (a-b)(a²-ab+b²). Cancel a-b to get a²-ab+b², with a≠b.

Cancel a-b across separate terms to get a²-b², with no restriction.

Factor a³-b³ as (a-b)(a²+ab+b²). Cancel a-b to get a²+ab+b², with a≠b.

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Curriculum context

Course: Math III
Standard: A-APR.4
Category: Algebra
Domain: Arithmetic with Polynomials and Rational Expressions
Objective: Prove polynomial identities and use them to solve or describe numerical relationships.
Problem type: Simplify a rational identity while preserving original-domain exclusions