Problem preview

A-APR.4 Warmup M3-004-A10-V04

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? \((x~-~4)(x~+~4)~=~x^2~-~16\)

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No, this is not an identity because it is true only when x = 4 or x = -4.

Yes, this is an identity because expanding (x - 4)(x + 4) gives x² - 16, which matches the right side for every x.

No, this is not an identity because expanding (x - 4)(x + 4) gives x² + 16, so the sign on the constant is wrong.

No, this is not an identity because the left side is factored and the right side is expanded, so they cannot be equal.

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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