Multiplying exponents... help...?

Question

Hi.

can someone help me with this?

I know that

(sqrt [a] - a) X (sqrt [a] - a) = (a - a^2)

but when I multiplied it out using FOIL, I got:

a - 2a^(3/2) + a^2 which does not equal (a - a^2)

I used a as the variable instead of x or else the multiplication sign would be confusing.

Please help me figure out what I did wrong here.


Thank you.

(sqrt [a] - a) X (sqrt [a] - a) = (a - a^2)

is true because multiplying things with same base increases the power.

ie, (a) x (a) = a^2

in this case, (a) = (sqrt [a] - a)

so it means (sqrt [a] - a)^2

and (sqrt [a])^2 --> a and (a)^2 = a^2

which is the answer (a - a^2)

Let me try to explain my situation.

I'm actually trying to find the critical points for the function :

f(x)= x sqrt(x - (x^2))

so I derived it correctly according to the textbook, but I can't seem to multiply it out...

if anyone could show me the steps I would be super grateful.


Thanks!!

I see what I did wrong now.

Thank you all I will try to remember to choose the best answer (the first one to reply with the correct answer)



THANK YOU ALL WHO REPLIED

Answer 1

You did right when you used the FOIL.

(sqrt [a] - a) X (sqrt [a] - a) ≠ (a - a^2)
But
(sqrt [a] + a) X (sqrt [a] - a) = (a - a^2)

Answer 2

First, let me gently tell you that your basic assumption is incorrect.

(a^1/2-a)(a^1/2-a) does not equal (a-a^2)

(a^1/2-a)(a^1/2+a) would equal (a-a^2)

The good news is that when you foiled it out,you got the correct answer.

Unfortunately, in this view I cannot see your additional comments, so I am going to have to go back and take another look at the rest of your problem.

Hang on.

You are trying to find the critical points of the function. Unfortunately, I don't remember what that means--give me a break, I'm old!

But if it means where f(x)=0, then it is a matter of setting each factor to zero.

so if f(x)=x(x-x^2)^1/2

f(x) = 0, when x=0, 1

Sorry I couldn't be of more help.

Answer 3

You FOILed correctly. But try

(sqrt [a] - a) * (sqrt [a] + a) = (use asterisk for multiply)

a + a^(3/2) - a^(3/2) - a^2 =

(a - a^2)

One's plus the second term, the other minus.

Answer 4

Okay here is the problem.
lets use simple letters
x = sqrt (a)
y = a

(x - y) (x - y) = x^2 + 2xy + y^2 .... eqn 1
(x - y) (x + y) = x^2 - y^2 .................eqn 2

You are taking LHS from eqn 1 and RHS from eqn 2
That is why you are not getting the correct answer.
I am assuming that you made a mistake while coping the problem. Recheck the signs in LHS and that should solve your problem

(sqrt [a] + a) (sqrt [a] - a)
= sqrt(a)[sqrt(a) - a] + a [sqrt(a) - a]
= [sqrt(a)]^2 - a sqrt(a) + a sqrt(a) - a^2
= sqrt(a)^2 - a^2
= a - a^2

Answer 5

The real problem here is that

[sqrt(a) -a] [sqrt(a)-a] is NOT, NEVER a-a^2 !

Your foil answer is actually correct.

Answer 6

Right church, wrong pew.
What you "know" isn't true. (sqrt(a) -a)(sqrt(a) + a) equals a-a^2. The FOIL multiplication is correct.

Answer 7

[ sqr(a) - a ] [ sqr(a) - a ] = a - a^2
[ sqr(a) - a ]^2 = a ( 1 - a )
a - 2 a sqr(a) + a^2 = a ( 1 - a )
a [ 1 -2 sqr(a) + a ] = a ( 1 - a ) . . . . cancel a
2 sqr(a) = 2a . . . . . . cancel 2
sqr(a) = a . . . . . square both sides
a = a^2 . . . . . . cancel a
a = 1