A student confused the model of a² − b² with (a − b)². Which area must be removed from a² − b² to obtain (a − b)²?

Correct answer: 2ab − b², the net area to remove

Direct answer: B. Keep the two expressions separate. The difference of squares is a² − b², while the square of a difference is (a − b)² = a² − 2ab + b². To change a² − b² into a² − 2ab + b², subtract the net amount (2ab − b²): (a² − b²) − (2ab − b²) = a² − b² − 2ab + b² = a² − 2ab. This wording concerns the signed region that must be removed from the original difference-of-squares arrangement; equivalently, the target expression contains the additional signed contribution −2ab + b² relative to a². Option B gives the positive amount removed. Option A states the signed contribution added in the target expression, not the positive area removed. Option C removes both original squares and destroys the expression. Option D removes only one ab strip and is incomplete. Memory cue: a² − b² and (a − b)² are different identities; the latter contains −2ab + b².