help with equation

[matty204359]

how was this formula simplified? what steps were taken to remove the 1/2 and where did the 2a or the exponents come from?

I'm trying to bone up on my physics but its been several years since my highschool physics. i used to be able to do this kinda thing so if someone could show/explain to me the steps maybe I'd start to remember it.

 

[mmm4444bot]

\(\displaystyle (U+W)(U-W) = U^2 - W^2\) as a special case of multiplying two binomials

This works the other way around, too.

A^2 - B^2 = (A + B)(A - B) is one of the special cases of polynomial factoring (see "Difference of Squares"). :cool:

 

[soroban]

Hello, matty!

\(\displaystyle d \;=\;\dfrac{1}{2}(x+y)\left(\dfrac{x-y}{a}\right) \;=\;\dfrac{(x+y)(x-y)}{2a} \;=\;\dfrac{x^2-y^2}{2a}\)

What steps were taken to remove the 1/2
and where did the 2a or the exponents come from?
. . Brrr . . . that gives me a chill!

I'm trying to bone up on my physics,
but it's been several years since my highschool physics.

It's not your high school physics that you've forgotten . . . it's basic algebra.

We have the product of three fractions: .\(\displaystyle \dfrac{1}{2}\cdot\dfrac{x+y}{1}\cdot \dfrac{x-y}{a}\)


Do you remember how to multiply fractions?
Multiply the numerators and multiply the denominators.
. . So we have: .\(\displaystyle \dfrac{(x+y)(x-y)}{2a} \)

Do you remember how to multiply polynomials?

 

[matty204359]

Hello, matty!


It's not your high school physics that you've forgotten . . . it's basic algebra.

Your correct, Its been quite a while since I've done any of this kind of math but its starting to come back to me. Some things I have read in this thread have helped me to remember a few things. I'm going to keep on this tho and the internet makes researching things easier.