In algebra, we know that:
(-a)² = positive result (read as: "negative a" squared)
...and...
-a² = negative result (read as: the negation of the product of "a squared")
Likewise, in algebra, we also know that:
(-4)² = 16 (read as: "negative 4" squared)
BUT WHAT I DON'T KNOW IS HOW TO SOLVE THIS:
-4² = 16 or -16 ?????
* I can’t determine if it would read “negative four squared” (which would be 16) or if it should read as “the negation of four squared” which would be -16
Any math geeks around?
What is the question?
If there isn't a space between "-" and "4" then it reads "negative 4 - squared" (-4)^2
If there is a space, then it's (4^2) then stick a negative in front.[/size]
The answer to the OP's question depends on context, that site doesn't understand contextual questions
Tom, I hadn't thought about the space.
Where the problem comes in is when I am simplifying an equation, and you want to put it in standard form, for instance:
16 - a²
-a² + 16
^ see?
That could be read as "negative a squared" or "the negation of the product of a squared", one yields a positive result and the other yields a negative result.
(2011-05-05, 03:41 PM)Time 2 Mobilize Wrote: [ -> ]Tom, I hadn't thought about the space.
Where the problem comes in is when I am simplifying an equation, and you want to put it in standard form, for instance:
16 - a²
-a² + 16
^ see?
That could be read as "negative a squared" or "the negation of the product of a squared", one yields a positive result and the other yields a negative result.
your simplification is ignoring the rules "Please Excuse My Dear Aunt Sally (PEMDAS)". if you put every item in ( ) then you will see the below is true.
16 - a² = -(a²) + 16
in your samples above, if a=4, the first is 0 the second is 32. The answer is 0
So, if I have this equation:
2a - 4²
and I reverse the order
does it become:
(-4)² + 2a = 16 + 2a
or
-(4²) + 2a = -16 + 2a
also, when you are presented with this term:
-4² (this is the actual crux of my confusion here, a negative constant with an exponent and no parenthesis anywhere)
is that "negative four squared" or 16
or...
is that "the negation of four squared" or -16
Like Tom said earlier, I am starting to suspect that "spacing" (in ^that instance^ is indeed the issue)
I really don't see the issue either way. Why are you working with the negatives anyway? Why not just make the equation all positive and then solve. That's the way I was taught and did it through out high school because it's just simpler.
Sorry, I have a tendency to overcomplicate things.
Here is my issue:
-4²
How do I read that? If you were given just that term, how would you read it? No space, no parenthesis...just THAT!
Is it "negative four squared", thereby equalling 16
Or, is it "the negative of the product of four squared", thereby equalling -16
read my post above
2a - 4² = (2a) - (4²) = 2a - 16