(x + 5)(x + 3) has a sum in the middle and a product at the end, and swapping the two is the commonest wrong line in Algebra 1. These free printable worksheets show it written out and ask which of four answers is right.
The two numbers do different jobs, and that is the whole idea. They add to make the middle coefficient and multiply to make the constant, so a student who remembers that both numbers appear but not which is which produces an answer that looks entirely plausible and is wrong by inspection only if you know what to check.
Why this sheet works
The four options separate the four failures: the middle term missing altogether, the sum and the product changed places, the last two numbers added rather than multiplied, and the brackets simply added. Choosing between them is naming which job was done to which number.
How this one works
One question from this sheet, worked through a step at a time.
Ana says (x + 5)(x + 6) − x² comes to 11x + 30. Which is correct?
(x + 5)(x + 6) − x²
(x + 5)(x + 6) − x²=x² + 11x + 30 − x²
(x + 5)(x + 6) − x²=x² + 11x + 30 − x²
(x + 5)(x + 6) − x²=11x + 30
(x + 5)(x + 6) − x²=11x + 30
they wrote:11x + 30
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 + 5)(x + 6) − x² becomes x² + 11x + 30 − x².
Tidy that up and it is 11x + 30.
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.
1Ana says (x + 5)(x + 6) − x² comes to 11x + 30. Which is correct?30x + 1130x² + 11x + 3011x + 30Why?
2Theo's answer to (x + 8)(x + 9) − x² is 17x + 17. Which is correct?x² + 17x + 7217x + 1772x + 1717x + 72Why?
3Noor wrote (x + 4)(x + 6) − x² = 10x + 24. Which is correct?x² + 10x + 242410x + 2424x + 10Why?
4Spot the mistake: (x + 7)(x + 8) − x² = 15x + 15. Which answer is right?15x + 1556x + 1515x + 56x² + 15x + 56Why?
Algebra reasoning · Multiplying two bracketsAnswer key
1. (x + 5)(x + 6) − x² = 11x + 30, which is what was written — this line is correct2. (x + 8)(x + 9) − x² = 17x + 72, not 17x + 17 (the two numbers were added where they should be multiplied)3. (x + 4)(x + 6) − x² = 10x + 24, which is what was written — this line is correct4. (x + 7)(x + 8) − x² = 15x + 56, not 15x + 15 (the two numbers were added where they should be multiplied)
