### Chapter 4: Algebra... Which is larger?

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

This question is compulsory.

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

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.
5x^2=5*(x*x), not (5*x)*(5*x)

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

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

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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1. Sorry refer to the second post.

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.

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.