grade 11 · A2-008

Recognize a polynomial identity

Match expanded and factored structures by distribution rather than surface resemblance.

Learn togetherFresh problem · seed 1900047945

Which expression is identically equal to \(x^2-4\)?

Let's work it out together.

Work through one checkpoint at a time. Your answer area opens after the reasoning.

Checkpoint 1

Recognize \(a^2-b^2\) as a difference of squares.
Checkpoint 2

Use conjugate binomials.
Checkpoint 3

Multiply the proposed factors to verify the middle terms cancel.

\((x-2)(x+2)\)\((x-2)^2\)\((x+2)^2\)\((x-4)(x+1)\)