### (8 March 2011) Chapter 4: Algebra... Which is larger?

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

This question is compulsory.

1. No, - x -=+ So that imagine the x is gone so the one that is 5x = -5x and -5x = 5x

2. No. X can be a negative number so it is not always the case where 5x^2 is larger.

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5. No, if x has a negative value, (-5x)^2 can be of greater value than 5x^2.

6. 5x^2 = 25x
(-5X)^2 =25
(Assuming x is positive number.
No. It is because when -5x is squared, the number with negative sign are multiplied by itself, which means that negative number multiplied by negative number must give a positive number, and positive number multiplied by positive number must also give a positive number, thus, the two numbers are of the same value.
But for some cases, x can also be a negative number so it could be the other way round from what Jennifer said in which 5x^2 is bigger. So Jennifer is wrong.

7. Yes, she is correct. 1st eg.5(2)^2=20. (-5(2))^2=100
2nd eg. 5(-2)^2=5(4)=20 (-5(-2))^2=100

8. No, I do not agree. That is because if X is a negative number so 5X^2 will become a negative and then it will be a smaller number than the other one.

9. No. X can be a negative number. Even if its not a negative number, assuming that both x's are the same, you can remove it.

5 to the power of two is EQUAL to the -5 to the power of two.

10. No as X could be a negative number.5X^2 will become a negative and then it would be smaller than the other one.

11. No it will always be the same because -5^2 is equal to 5^2

12. No. x can be any number and it will still be equal.
If it is a negative number, it would change the first expression to negative before it is squared but after its squared it becomes positive.
If it is a positive number the second expression would be negative before it is squared but after its squared it also becomes positive.

13. No. they are both 25x^2 when simplified

14. No, as negative times negative is equals positive, so it should be equal.

15. No X can be a negative number so 5x^2 would be come negative number thus, smaller than (-5x^2)

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17. No.I do not agree. If x is 2 then 5x^2 is equal to 100 but (-5x)^2 is equal to 100. This is because x in both equations is the same whether it is positive or negative.

18. No, both of the above equations are equal.

19. Dawn

No.
Lets take the first example as x = 10.
(5x)^2= 2500
(-5x)^2=2500.They are equal, thus "(5x)^2" is not smaller than "(-5x)^2".

The second example, lets take x=15
(5x)^2=1125
(-5x)^2=5625
In this case, (5x)^2 is indeed smaller than (-5)^2

20. No, x could be a negative number and (assuming x is -1)5x^2 would be equal to (-5x)^2.

21. Assuming that x is 2.
[(5)(2)]^2 = 100
[(-5)(2)]^2 = 100

Assuming that x is -2.
[(5)(-2)]^2 = 100
[(-5)(-2)]^2 = 100

I do not agree. [(5)(2)]^2 and [(-5)(2)]^2 have the same value, just like [(5)(-2)]^2 and [(-5)(-2)]^2.

5x^2 is not always the same as (-5x)2.

22. Yes, as if x=2, 5(x^2) is actually 5x4=20 but for the other (-5x)^2, it will give 100 which is more than the 5x^2

23. E U G E N E V O O3/08/2011 11:31:00 AM

No she is wrong as -*- is positive as well as +*+.

24. Not if "x" is a negative no.

25. No, I don't. Both sum 's answer is the same.