(−3)² vs −3²: the parenthesis that changes the sign
Substituting x = −3 into x² should give 9. Type −3² into a calculator and it says −9. Both facts are true — and that's the trap.
Why it happens
Exponents bind tighter than the minus sign. Without parentheses, the square applies to 3 first and the negation comes last.
See the trap
Evaluate f(x) = x² − 2x at x = −3.
−3² − 2(−3) = −9 + 6 = −3.
(−3)² − 2(−3) = 9 + 6 = 15.
How to actually fix it
- 1Substituting a negative? Wrap it in parentheses every time.
- 2Read −x² as −(x²), never (−x)².
- 3On calculator sections, type the parentheses explicitly.
FAQ
Does this matter for even exponents only?
Odd powers keep the sign either way, so the trap only bites on even powers — which is why x² problems feature it constantly.
How do I stop repeating this mistake?
Reading the explanation isn't enough — your brain needs to beat the trap on a fresh question. Practice the skill in the kaoshen.co question bank: miss one and it is logged with the exact error, then brought back to you three days later and again after fourteen.
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