confused14? said:
considering these expressions -x2 and (-x)2 are they the same? i'm lost. please expain :?: :?:
-x<SUP>2</SUP> and (-x)<SUP>2</SUP> are
not the same. Here's why:
Remember the order of operations? First, you do any operations inside parentheses. Next, you do powers or roots (exponents).
-x<SUP>2</SUP> has no operations in parentheses. So, you start by doing the squaring. THEN you find the opposite of the result.
For example, if x = 3, -x<SUP>2</SUP> would become -3<SUP>2</SUP> Start by squaring 3 to get 9. Then, find the opposite of 9, which is -9. So -3<SUP>2</SUP> = -9.
Or, if x = -5, -x<SUP>2</SUP> would become -(-5)<SUP>2</SUP>. Multiply (-5)(-5) to do the squaring. (-5)(-5) is 25. Then, find the opposite of 25, which is -25.
(-x)<SUP>2</SUP> DOES have an operation inside the parentheses....it says "take the opposite of whatever x is." You do that first. THEN you do the squaring.
For example, if x = 3, then (-x)<SUP>2</SUP> becomes (-3)<SUP>2</SUP>. The opposite of 3 is -3, and when you square -3, you do (-3)(-3) and get 9.
Or, if x = -5, then (-x)<SUP>2</SUP> becomes [-(-5)]<SUP>2</SUP>. The opposite of -5 is 5....now you have (5)<SUP>2</SUP>, or 25.
For any real, non-zero value of x, -x<SUP>2</SUP> is always negative. And (-x)<SUP>2</SUP> is always positive.