grade 11 · A2-008

Recognize a polynomial identity

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

Learn togetherFresh problem · seed 302668260

Which expression is identically equal to \(x^2-25\)?

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.

\((x-5)^2\)\((x+5)^2\)\((x-25)(x+1)\)\((x-5)(x+5)\)