Prove polynomial identities and use them to solve or describe numerical relationships.
Verify and apply the difference-of-squares identity
Problem
Verify \((a~-~b)(a~+~b)~=~a^2~-~b^2\) by expanding the product.
Big Picture
What this problem is really about
Conjugate factors contain the same two terms but opposite signs, and that sign pattern is the reason the identity works. Expand all four products while keeping each sign attached to its term. The two cross products then have equal magnitude and opposite signs, so their cancellation leaves the square terms to compare.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
