(x + 5)² is not x² + 25. The middle term is the one that goes missing, and it goes missing for almost everybody once. These free printable worksheets show the wrong line and ask which of four answers is correct.
Squaring a bracket looks like it should distribute over the plus, and it does not — that expectation is so natural it has a nickname among teachers. Writing the bracket out twice, as (x + 5)(x + 5), is what makes the two middle terms appear, and a child who has seen where they come from stops losing them.
Why this sheet works
The four answers separate the near-misses that matter: no middle term at all, a middle term that was never doubled, a constant that was never squared, and a bracket that was doubled instead of squared. Each is a different misunderstanding and the correction for each is different.
How this one works
One question from this sheet, worked through a step at a time.
Noor says (x + 7)² − 49 comes to x² + 14x. Which is correct?
(x + 7)² − 49
(x + 7)² − 49=x² + 14x + 49 − 49
(x + 7)² − 49=x² + 14x + 49 − 49
(x + 7)² − 49=x² + 14x
(x + 7)² − 49=x² + 14x
they wrote:x² + 14x
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.
On your own, and writing the step nobody writes down: (x + 7)² − 49 becomes x² + 14x + 49 − 49.
Tidy that up and it is x² + 14x.
Now compare — and this time the two agree. The line on the page was already right, which is a finding, not a missing mistake. Some of them are.
Read each line of working and choose the answer that is correct.
1Noor says (x + 7)² − 49 comes to x² + 14x. Which is correct?x² + 14xx²x² + 7xx² + 14x + 49Why?
2Sam says (x + 3)² − 9 comes to x² + 6x. Which is correct?x² + 6xx² + 6x + 9x² + 3xx²Why?
3Noor wrote (x + 4)² − 16 = 2x − 8. What should it be?x² + 8xx² + 8x + 16x² + 4x2x − 8Why?
4Check this line: (x + 8)² − 64 = x² + 8x. Which is correct?x²x² + 16x + 64x² + 8xx² + 16xWhy?
Algebra reasoning · Squaring a binomialAnswer key
1. (x + 7)² − 49 = x² + 14x, which is what was written — this line is correct2. (x + 3)² − 9 = x² + 6x, which is what was written — this line is correct3. (x + 4)² − 16 = x² + 8x, not 2x − 8 (the bracket was doubled instead of squared)4. (x + 8)² − 64 = x² + 16x, not x² + 8x (the middle term was not doubled when the bracket was squared)
