Chapter 4: Algebra... Which is larger?

Jennifer says, "5x2  is always smaller than  (-5x)2. "

Do you agree? Explain your answer. 
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15 comments:

  1. Let x=5,
    5x5^2=125
    (-5x5)^2=625
    Thus, 5x^2 is smaller than (-5x)^2. Assuming that x is a natural number, whole number and rational number.

    Will try to find x if 5xx^2=(-5xx)^2

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    Replies
    1. Please reply so I know if I did it correctly!

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    2. Also assuming the number is not 1!

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    1. Wrong calculation,
      If x=1,
      5*1^2=5 and (-5*1)^2=25
      Thus, they are both not the same.
      Your errors:
      5x^2=5*(x*x), not (5*x)*(5*x)

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  3. No.
    As 5x^2=25x^2
    and
    (-5x^2)=25x^2 as well

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  4. No, as 5x^2 is equivalent to (-5x)^2:
    5x^2= 5x*5x
    (-5x)^2= -5x*-5x
    =
    5x*5x= -5x*-5x
    Hence,
    5x*5x= 5x*5x

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  5. Jennifer is correct.
    5x^2 = 5x^2
    (-5x)^2 = 25x^2 ( note that when negative * negative will give you a positive number.)
    Thus, (-5x)^2 is greater than 5x^2 . ( note that even if x is a negative number, after x is being square rooted, x will still be a positive number).

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  8. It depends. If x is 10 , then 5x10x10=500 But -50x-50=250. If x is 0, then everything is 0. So with the exception that x is 0, then they are the same.

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  10. Jennifer is wrong. 5x^2 is the same as (-5x)^2.
    Lets take x as 1.
    First equation:5(1)^2=25.
    Second equation:(-5(1))^2=25.
    To confirm this lets do another example, lets take x as 5.
    First equation :5(5)^2=625
    Second equation:(-5(5))^2=625
    Therefore, Jennifer is wrong.

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  11. Yes, with one exception.

    5x^2
    =5*x*x

    (-5x)^2
    =(-5)*(-5)*x*x
    =25*x*x

    But if x=0

    5x^2
    =5*0*0
    =0

    (-5x)^2
    =25*0*0
    =0

    5x^2 and (-5x)^2 would be equal.

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