Prove polynomial identities and use them to solve or describe numerical relationships.
Decide whether a polynomial equation is an identity by expanding both sides
Problem
Does this statement hold for all variable values? \((x~+~2)^2~=~x^2~+~4x~+~4\)
Big Picture
What this problem is really about
To test a statement for all variable values, turn both sides into comparable polynomial forms. Expand the squared binomial with both cross products, combine like terms, and compare the coefficients of matching powers. If the resulting polynomials agree term for term, the equality follows from algebra for every input rather than from a few examples.
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.
