Why is -5^2 and (-5)^2 different?

[samalex]

Hi,
I'm working through my Algebra homework, and while working out the quadratic equation to factor a trinomial the b=-5, but i've noticed that on my calculator I get (-5)^2 = 25 while -5^2 = -25. I would've thought each equaled 25 with there being no difference in th two, but it's like -5^2 is acting like -1 * 5^2 to simply to -1 * 25 then -25. This has me very confused now... Can someone explain why (-5)^2 and -5^2 would be different?

Thanks --

Sam

 

[pka]

Hi,
I get (-5)^2 = 25 while -5^2 = -25. I would've thought each equaled 25 with there being no difference in th two, but it's like -5^2 is acting like -1 * 5^2 to simply to -1 * 25 then -25. This has me very confused now... Can someone explain why (-5)^2 and -5^2 would be different?

Any real number squared is non-negative.
That is \(\displaystyle x^2\ge 0\) if \(\displaystyle x\in\mathbb{R}\).

The notation \(\displaystyle -x\) stands for the negative of \(\displaystyle x\).
Thus \(\displaystyle -x^2\le 0\) if \(\displaystyle x\in\mathbb{R}\).

Thus \(\displaystyle (-5)^2>0~\&~-5^2<0.\)

 

[lookagain]

Hi,
I'm working through my Algebra homework, and while working out the quadratic equation to factor a trinomial the b=-5,
but i've noticed that on my calculator I get (-5)^2 = 25 while -5^2 = -25.

Sam

samalex, when you put the values or a, b, and c into the Quadratic Formula,
make sure there are parentheses around the b value. Also, it is more
consistent to place grouping symbols around all of the values subbed in:



\(\displaystyle x \ = \ \dfrac{-(b) \pm \sqrt{(b)^2 - 4(a)(c)}}{2(a)}.\)

 

[burakaltr]

Hi,
I'm working through my Algebra homework, and while working out the quadratic equation to factor a trinomial the b=-5, but i've noticed that on my calculator I get (-5)^2 = 25 while -5^2 = -25. I would've thought each equaled 25 with there being no difference in th two, but it's like -5^2 is acting like -1 * 5^2 to simply to -1 * 25 then -25. This has me very confused now... Can someone explain why (-5)^2 and -5^2 would be different?

Thanks --

Sam

Please Remember :

(x*y)**2 = (x**2)*(y**2)

So -5=-1 * 5
squaring both sides

(-5)**2=(-1)**2 * (5**2)=1*25

= + 25