Exercises: Prove and Use Polynomial Identities

Work through each section in order. For proof problems, show all algebraic steps clearly.

Grade 9·22 problems·~38 min·Common Core Math - HS Algebra·standard·hsa-apr-c-4

Work through problems with immediate feedback

Fluency Practice

A student wants to prove that $(x + y)^2 = x^2 + 2xy + y^2$ is a polynomial identity. Which approach is mathematically valid?

Test 5 different values of $x$ and $y$ , confirm the equation holds for each, and conclude it is an identity.

Expand $(x + y)(x + y)$ algebraically to get $x^2 + 2xy + y^2$ , confirming the two sides are equal as expressions.

Set the two sides equal and solve for $x$ to find all values where it holds.

Verify with $x = 0$ and $y = 0$ only, since zero is the simplest test.