formula

[shahar]

I don't know why the end formula is as it is.
Can somebody show we the missing step to it

 

[Dr.Peterson]

Here are two ways you might discover what they did:

1. Factor [MATH]1 - r^2[/MATH], then simplify.
2. Try working backward from the final form, rationalizing the denominator, and you should get the previous form.

It's interesting, though, that the final form is not what we normally call "simpler". I imagine that in context there is a reason for preferring that form, and that might provide the motivation for what they did.

 

[shahar]

How do I factorized (1 - (r^2))
...I think by the formula:
(a - b)^2 = (a+b)(a-b)
But I don't see it. O.K.?

 

[topsquark]

Maybe you need to tell us the rest of the problem. We can't do this in a vacuum.

Now, \(\displaystyle (a - b)^2 \neq (a + b)(a - b)\). (FOIL the LHS.)

What you need to say is that \(\displaystyle a^2 - b^2 = (a + b)(a - b)\).

-Dan

 

[Otis]

Hi shahar. Note the denominators. The expression 1 - r does not begin inside a radical sign. We need to introduce the radical.

To rewrite 1 - r as a radical expression, we need √[(1 - r)²].

Does that help?

?

 

[shahar]

What Dan [Topsquark] say help me see it.
Thanks...