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I know that (-2)^2 = 4 and -2^2 = -4.

However, I do not know what y^2 is when y is a negative number. Is it -y or (-y)?

I'm asking because I got the following question wrong:

a = -2, b = 6

What is a^2 - b?

I substituted the question as follows:

-2^2 - 6 = -10

However the answers was -2, indicating that it should have been substituted like this:

(-2)^2 - 6 = -2;

There were no brackets in the original question. Does that mean that when you substitute a variable with a negative number that it's bracketed by default?

OwenAlexander
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    Well yes, $a$ is a single object, so it is "bracketed by default." – Doug M Aug 31 '16 at 22:25
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    Yes, whenever you substitute anything it is bracketed by default. We often don't even bother bracketing and showing that inbetween step because it is so second nature. Consider the expression $5x+2$. If we wanted to give that expression a name, say $y$, and then multiply the expression by two, we would have $(5x+2)\cdot 2$, not $5x+2\cdot 2$. I.e. $y\cdot 2 = (5x+2)\cdot 2$ not $y\cdot 2 = 5x+2\cdot 2$ – JMoravitz Aug 31 '16 at 22:25

1 Answers1

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The problem is that $-2^2$ means $-(2\times2)$. $(-2)^2=-2\times-2$. The latter of these $2$ representations is $-2$ squared.

Mike
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