What is -x squared

Answer 1

This is a question that regularly comes up in my classroom.

(-x)² = (-x)(-x) = x² or (-1)²(x)² .......the squared goes to what's directly in front it. Since there are parentheses it goes to everything in the parentheses.

-x² = -(x²) so it remains -x² .... the squared only goes to the term directly in front of it which in this case is only x

When using a calculator, be sure to include parentheses when they are needed otherwise you will get an incorrect answer.

Hope this helps clear up what truly is a confusing concept.

Answer 2

If you're still a little puzzled, maybe using a particular number rather than a variable will help.

If you see -3², the PEMDAS rule says work inside of parens first, then look for exponents and do those. We don't have parens here, so we square 3, THEN apply the minus sign. The result: negative 9.

But if you see (-3)² we must first apply the minus sign within the parens so that what we're squaring is a negative 3. The result: negative times negative gives positive, so the result is positive 9.

I suppose that the moral of the story is: when in doubt, use parentheses to say what you mean.

Answer 3

(-x)²= (-x)(-x) = x²

Answer 4

Could be written in two ways - that's why grouping symbols are helpful

It could be either (-x)² or -x². Math is more precises than English.