Math question: X^2 + Y / 3Y?

Question

x = -5, y = -3

I'm aware that the answer is 22/-9, however my algebra prof marked my answer wrong because in doing the work I did not solve it like this: (-5)^2 + (-3) / 3(-3). Instead I solved it like this: -5^2 + (-3) / 3(-3). He claims that the parenthesis around the -5 are necessary for the answer to be correct. Is this true?

Answer 1

It sure is necessary. -5^2, without parentheses, means do exponentiation first, since that outranks taking the negative of a number. You get 5^2 = 25, and then negating that gets you -25, so -5^2 = -25. Similarly, -(5^2) means do what's in the parentheses first. So you get the negative of 25, or -25.

But (-5)^2 is different. That means negate the 5 first. -5. Then square it: (-5)*(-5) = +25. So you get +25.

So which do you use above? The expression x^2 means whatever x is, square it. So if x = -5, this means take whatever -5 is, and square it. The result is +25. To indicate that, when you substitute a negative number in for x, you need to put it in parentheses, so x^2 becomes (-5)^2.

Answer 2

the () are needed because they denote the order of operations that are used. (-5)^2 is +25 because negative five time negative five is a positive number. However -5^2 yields positive five times positive five, while retaining the negative to be put on after the term is squared. It is only decided by convention that this is true as a means of showing the difference between the two.

Answer 3

he is right.

-5^2 = - 25 and
(-5)^2= 25

when you do not put the parenthesis you square only 5. as you do not square the minus, it remains.

when you put the parenthesis you square -5. now that you have squared the minus too it becomes positive. so these give different results. hope you understand now and wont goof up again! :)

your equation asks you to square "x", so you have square the whole "x" ie -5

by the way, the correct answer should be 76/ 3

Answer 4

yes he is right, (-5)^2 = 25 while -5^2= -25 because -5^2 = -1 x 5^2 the right answer is 25/3

Answer 5

-5^2 = -25
(-5)^2 = +25

Answer 6

somewhat true.
-5^2 = -25
(-5)^2 = 25

Answer 7

yea becuz otherwise you will get a (-1)25 +(-3)...
Laws of exponents man you gotta do it by the book
the way you do it you make it (-1)*(5)*(5)
Parentheses
Exponents
Mult
Div
Add
sub

Answer 8

I doubt it but it's probably the way he solves it and wants to teach his students, so the easiest thing is to play along until you're out of the class. sorry!