Explaination request

[jimbir]

I'm reading a book called "conquering Calculus" by Jeff Weaver.
On page 215 he presents the following formula:
576 - 16(6 - Dx)^{2 =} Dy² (I don't know how to insert a delta symbol so I'm using a capital D)

He then starts a simplification process.
1st step 576 - 16(36 - 12Dx + Dx²) = Dy (please explain where the 12Dx came from)

2nd step 576 - 576 + 192Dx - 160Dx² = Dy (please explain where the 160Dx² came from. My guess is it's a typo and should be 16Dx²)

The last step 192Dx - 16Dx² = Dy (please explain how the 160Dx₂ became 16Dx². I could understand this if my guess above is correct.Which would leave only my confusion about the 12Dx in step 1)

If someone can lead me to a link that explains how this simplification process works, I'll be glad to study it and learn how it's done. (The best way to learn anything...)

Thanks. Jim Birke

 

[stapel]

...On page 215 he presents the following formula:
576 - 16(6 - Dx)2 = Dy2 (I don't know how to insert a delta symbol so I'm using a capital D)

He then starts a simplification process.
1st step 576 - 16(36 - 12Dx + Dx2) = Dy (please explain where the 12Dx came from)

You were supposed to have taken algebra ("pre-calculus") before you were put into calculus. If you had, you'd have learned about multiplying polynomials. To learn now, try here.

Once you have studied the lesson (in particular, the part about squaring binomials), try to do the expansion yourself:

. . . . .\(\displaystyle (6\, -\, \Delta_x)^2\, =\, (6\, -\, \Delta_x)(6\, -\, \Delta_x)\, =\, ...\)

2nd step 576 - 576 + 192Dx - 160Dx2 = Dy (please explain where the 160Dx2 came from. My guess is it's a typo and should be 16Dx2)

You are correct; the "160" is a typo.

The last step 192Dx - 16Dx2 = Dy....

If someone can lead me to a link that explains how this simplification process works, I'll be glad to study it and learn how it's done.

To learn about adding polynomials, try here.

If you get stuck, please reply showing all of your steps. Thank you!

 

[jimbir]

Thank you both for the help.

As soon as I saw how Stapel simplified the term (6-Dx)² as (6-Dx) (6-Dx) , I knew what I had missed. I'm happy you both agreed that the 160Dx² was a typo.

By way of explanation of what I'm doing. I checked a book out of the library about Issac Newton. In it, the subject of calculus, of course, came up. My 77 year old brain said "why not?" so I checked out several books in the genre of calculus for dummies (including the one I mentioned below). I then realized I had forgotten everything I learned in algebra class 61 years ago. So, back to the library for some books on algebra. After I get refreshed on that subject, I'll get back to calculus.

I'm glad I found this site. It promises to be helpfull

Question. How do I insert the delta icon in my posts?

 

[Ishuda]

...Question. How do I insert the delta icon in my posts?

Generally people use LaTex, see
ftp://ftp.ams.org/pub/tex/doc/amsmath/short-math-guide.pdf
for example which also has more links.

On this site you put the LaTex commands betweeen the tag pairs [ tex ] [/ tex ] (without the spacing). For example

[tex]\text {This is a small and large delta}\, \delta\,\, \Delta[/tex]

produces
\(\displaystyle \text {This is a small and large delta }\, \delta\,\, \Delta\)

The \, is a space