Jennifer says, "

*. "*

**5x**^{2}is always smaller than (-5x)^{2}**Do you agree? Explain your answer.**

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Yes, I agree.

ReplyDeleteLet's break these down to their prime factors first.

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

Where as

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

As you can see, in 5x^2, x*x (or x^2), is multiplied by 5 once.

However, in 5x^2, it is multiplied by 5 twice (or 5^2).

Is there any exceptional cases?

Deleteyes, if x is greater than 0∪x<0

DeleteFor example we take (x) to be 2,

ReplyDelete5 x 2 x 2= 20

(-5 x 2) (-5 x 2)

= 100

This shows that (-5x)^2 is larger than 5x^2 and so I agree with Jennifer.

Have you tested it with enough numbers to conclude?

Delete