Multiplying two brackets, step by step

(x + 5)(x + 3) has a sum in the middle and a product at the end.

The question

Spot the mistake: (x + 2)(x + 8) − x² = x² + 10x + 16. Which answer is right?

(x + 2)(x + 8) − x²

(x + 2)(x + 8) − x²=x² + 10x + 16 − x²

(x + 2)(x + 8) − x²=10x + 16

they wrote:x² + 10x + 16

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 + 2)(x + 8) − x² becomes x² + 10x + 16 − x².
Tidy that up and it is 10x + 16.
Now compare. They wrote x² + 10x + 16, and the x² was never taken away again — so the correct answer is 10x + 16.

How it works.

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.
02
On your own, and writing the step nobody writes down: (x + 2)(x + 8) − x² becomes x² + 10x + 16 − x².
03
Tidy that up and it is 10x + 16.
04
Now compare. They wrote x² + 10x + 16, and the x² was never taken away again — so the correct answer is 10x + 16.