(-x) ^2 is not equal to -x^2. Why?

Question

(-x) ^2 is not equal to -x^2. Why?

Answer 1

order of precedence.  You do ^ before negation.

a - times a - (squaring) is a positive.

- x^2 is a X(be it negative or positive) times itself is a positive, then you negate and it becomes a negative.

Answer 2

Offtopic: if index is double-digit the answer always loose minus.

(-x) ^2 = x^2

-x ^2 = -x ^2

if minus is brackets, and index is double-digit (2,4,6...) then it remove minus

Answer 3

Say x=2

(-x)^2

=(-2)^2

=4 (because the negative is also squared)

-x^2

=-2^2

=-4 (because only the x (2) is squared)

Answer 4

(-x)^2

= (-x)(-x)

= x^2

-(x^2)

= -1 * x^2

= -x^2

∴ (-x)^2 ≠ -x^2

Answer 5

Cause of the bracket

Like DUHHHHH

LOL!!

Answer 6

The person above me is right.

Basically:

(-x)^2 = -x times -x = positive (remember, when you multiply two negative numbers, the product is a positive number)

-x^2 = -x times x = negative (think of this as the opposite of x^2)

Answer 7

(-x)^2 = (-x) * (-x) = x^2, which is a positive number except when x=0.

-x^2 is a negative number except when x=0.

Answer 8

Mathmani has it right. By definition,  (-x)^2 equals (-x)*(-x) which equals x^2. That is the reason. (This has nothing to do with order of operations, etc. It's a question of knowing what something really means by definition.)

Answer 9

Well I know the french word. PEDMAS.

Paranthese

Exponentielle

Division

Multiplication

Addition

Soustraction

That's the order of how you're supposed to solve an algebra equation.

So in the first case, you multiply the entire parenthesis by 2. In the second case, there is no parenthesis, therefore the next in line is exponential. You have to do the exponential 2 and then make it negative.

Don't forget that a double negatif = a positif.

Say x = 2

(-x) ^ 2 = (-2) ^ 2 = 4

- x ^ 2 = - 2 ^ 2 = - 4

That's the difference. Hope this was helpful :).

Answer 10

because square of a random number no matter its positive or negative.........the answer is always positive....................

so (-x)^2 is positive

x^2 is positive but we have the negative sign in front of it.........so that is negative

so (-x)^2 never is equal to -x^2