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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,534

I have written a general page on Solving Equations

Feedback welcome ... please

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,032

Hi MathsisFun;

Good page. Helped me a lot with the geometric representation.

Those 3 basic forms

(a+b)(a+b)

(a-b)(a-b)

(a+b)(a-b)

are also the basis for mental arithmetic. Lets take your example:

If you wanted to multiply 38 * 42 you could use that form with y=10.

Answer 16*100 - 4 = 1596 like magic.

For 63 * 57

63*57 = 36 * 100 -9 = 3591

With a little practice and algebra, you can do lots of arithmetic in your head.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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