Problem preview

A-APR.4 Warmup M3-004-A10-V02

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

Decide whether a polynomial equation is an identity by expanding both sides and comparing

Problem

Is this equation an identity? \((x~+~1)^2~=~x^2~+~1\)

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No, this is not an identity because expanding (x + 1)² gives x² + 2x + 1, so the right side is missing the 2x term.

No, this is not an identity because the equation is true only when x = negative one-half, not for every value of x.

Yes, this is an identity because squaring x + 1 gives x² + 1, which matches the right side exactly.

No, this is not an identity because the two sides are written differently, so they cannot represent the same expression.

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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: Decide whether a polynomial equation is an identity by expanding both sides and comparing