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

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

This question is compulsory.

1. No. Firstly, 5x^2=25x,
And,(-5x)^2=25x
So the answers are the same. Hence, they are equal. So Jennifer is wrong...

2. No , 5x^2 is 25x and (-5x)^2 is also 25x so both of them have the same value

3. No. because as long as the number is squared,the negative and positive number give the same answer. In this example, both expressions equals to 25x.

4. No I do not. 5x^2 is 5x x 5x which is 25x. (-5x)^2 is -5x x -5x which is 25x.
Thus, both expressions are equal.

5. No. 5x^2 is 25x and (-5x)^2 is also 25x since -*-=+ so both of them are equal.

6. Nope. Both give the same answer as when a negative number multiplies a negative number we will get a positive numbers. Thus both will give25x

7. Mark :) :( :&#39;( (^^^) :D :O :42: O:) :p 3:)3/08/2011 12:31:00 PM

NOOOOO. 5x^2 = 25x (-5x)^2=25x This is because when a positive number multiplies with a positive number, the product is positive. This goes the same for negative numbers, therefore, Jennifer is wrong and they are both equal.

8. No, I do not agree as 5x^2 is 25*x^2, and (-5x)^2 is also equal to 25*x^2.
So they are equal and Jennifer is wrong.

9. No I do not agree. As 5x^2=25x and (-5x)^2=25x, both answers are the same. It is because negative multiplied by negative gives positive.

10. No, I do not agree because the product of two numbers with the same sign(+ or -) would always be a positive number. Therefore, 5x*5x would be the same as -5x*-5x.

11. No, I do not agree. If x=0, 5x^2= 0 and (-5x)^2=0, thus they are equal.
~Nina

12. No, I do not agree. If x=0, then 5*x*x=0 and -5x*-5x=0. Thus, the expressions may have the same value.

13. "5x^2 is always smaller than (-5x)^2. "

I do not agree.

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

25x can also be expressed 5*5*x

5*x*x could have a bigger value than 5*5*x depending on what the value of x is.

For Example
-In a Case in which 5x^2 is bigger than (-5x)^2:
Let x be 10.
5*x*x
=5*10*10
=500

5*5*x
=5*5*10
=250

500 is more than 250 which also proves that 5x^2 is not always smaller than (-5x)^2 depending on x.

14. ok i just realised how long my "comment" is im really sorry...

15. No, I do not agree.

Eg: Let x be the numer 2.

1. 5x^2=5*2^2 2.(-5x)^2=(-5*2)^2
=10^2 =(-10)^2
=100 = 100

The value of the simplified expressions is the same so the statement Jennifer says is wrong.

16. No, I do not agree.
5x^2=25x
(-5x)^2=25x
As a positive number multiple another positive number, the answer will be positive.
As a negative number multiple another negative number, the answer will be negative.

17. But the 5x^2 can also be 5(x^2) according to order of operations, "in the power of" is before multiplication and division. So, as the negative has brackets to indicate we must do the multiplication before the "powers". Therefore, we must put brackets to indicate the multiplication 1st.

In the end,as negative still brings positive and positive brings positive.

Example: 5a^2. Let a be 4. So, 5*4^2 which 20*16 and thus comes out 160. But negative..... (-5a)^2=(-5*4)^2=(-20)^2 so comes out 40 lesser than the positive.

This is an exception.

18. BTWFYI, I am Owen. (Forgot)

19. No, I do not agree. 5x^2=25x
And...(-5x)^2=25x

Positive no. x Positive no. = Positive no.
Negative no. x Negative no. = Positive no.

20. I disagree with her.
5x^2= 25x
(-5x)^2=-5x x -5x
=25x
So, the number is the same.

21. This comment has been removed by the author.

22. I disagree. 5x^2=25x while (-5x)^2=25x as well. Thus, 5x^2 is not smaller than (-5x)^2, but they are of equal value.