Squaring a binomial, step by step

(x + 5)² is not x² + 25.

The question

Ana wrote (x + 5)² − 25 = x² + 10x + 25. Which is correct?

Ana wrote (x + 5)² − 25 = x² + 10x + 25. Which is correct?

(x + 5)² − 25
(x + 5)² − 25=x² + 10x + 25 − 25
(x + 5)² − 25=x² + 10x + 25 − 25
(x + 5)² − 25=x² + 10x
(x + 5)² − 25=x² + 10x
they wrote:x² + 10x + 25
  1. Do not check by reading their line. Somebody else's working is the most persuasive thing on the page, and rereading it is how you end up agreeing with it — do the step yourself first, then compare.
  2. On your own, and writing the step nobody writes down: (x + 5)² − 25 becomes x² + 10x + 25 − 25.
  3. Tidy that up and it is x² + 10x.
  4. Now compare. They wrote x² + 10x + 25, and the squared constant was never taken away again — so the correct answer is x² + 10x.

How it works.

  1. 01

    Do not check by reading their line. Somebody else's working is the most persuasive thing on the page, and rereading it is how you end up agreeing with it — do the step yourself first, then compare.

  2. 02

    On your own, and writing the step nobody writes down: (x + 5)² − 25 becomes x² + 10x + 25 − 25.

  3. 03

    Tidy that up and it is x² + 10x.

  4. 04

    Now compare. They wrote x² + 10x + 25, and the squared constant was never taken away again — so the correct answer is x² + 10x.