Help with algebra relating to pythagorean theorem

Question

question im trying to work the Pythagorean Theorem out and how im doing it is use a right angle triangle with the side lengths of 3 and 4 and trying to solve for the hypontenuse 5^2. now im making a square with the lengths of the hypontenuse by putting 4x 3,4,5 triangles in a square formation now to work out the square in the middle ive gotten (a+b)^2-2(a*b)=c^2 now i know this translates to a^2+2(a*b)+b^2-2(a*b)=c^2 which also translates to a^2+b^2=c^2 my problem is i dont understand why the equation i got (a+b)^2-2(a*b)=c^2 translates to the other two, obviously my lack of knowledge on the rules of algebra but if anyone can help me that would be AWESOME!

Answer 1

Various proofs are at:

http://jwilson.coe.uga.edu/EMT668/EMT668.Student.Folders/HeadAngela/essay1/Pythagorean.html

 

One of which is your "square" proof.

Answer 2

HYPOTENUSE is the correct spelling of the longest side in any right triangle.

 

If you have (a+b)² - 2ab = c² then the rule of expansion for the squared binomial gives a² - 2ab + b²

and therefore you wind up with a² + b² = c²

and that, sir, is the point of the Pythagorean Theorem.

 

YOU CAN prove the rule that I quoted for the square of the binomial a+b by doing "FOIL":  (a+b)(a+b)