Thursday, 20 February 2014

Algebra... Which is larger? (II)

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

Do you agree? Explain your answer. 

Enter your response in Comments.

This question is compulsory.


  1. Yes, I agree.
    Let'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).

  2. For example we take (x) to be 2,

    5 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.

    1. Have you tested it with enough numbers to conclude?