Question

Hello another tutorial :)
on algebraic identities

Answer 1

ALGEBRAIC IDENTITIES :

Hello friends , algebraic identities are one of the most important part of mathematics . Today I am going to tell you all the Proof of algebraic identies also .

1) \(\large{(a+b)^2=a^2+2ab+b^2}\)

\[\large{(a+b)(a+b) = a(a+b)+b(a+b) = a(a)+a(b)+b(a)+b(b)}\]
\[\large{(a+b)^2=a^2+ab+ba+b^2}\]
\[\large{(a+b)^2=a^2+2ab+b^2}\]

Let me mention some properties that i used here :

1) Commutative property : ab = ba
2) Distributive property under addition : (a+b)(a+b) = a(a+b)+b(a+b) ==> a(a)+a(b)+b(a)+b(b)

these properties will be used in the coming indentites also .

2) \(\large{(a-b)^2=a^2-2ab+b^2}\)

\[\large{(a-b)(a-b)=a(a-b)-b(a-b) = a(a)-a(b)-b(a)-b(-b)}\]
\[\large{(a-b)(a-b)=a^2-ab-ba+b^2}\]
\[\large{(a-b)(a-b)=a^2-2ab+b^2}\]

3) \(\large{a^2-b^2=(a-b)(a+b)}\)

can i write the above equation as :
\[\large{(a+b)(a-b)=a^2-b^2}\]
\[\large{a(a-b)+b(a-b) = a^2-b^2}\]
\[\large{a(a)-a(b)+b(a)+b(-b)=a^2-b^2}\]
\[\large{a^2-ab+ba-b^2=a^2-b^2}\]
\[\large{a^2-b^2=a^2-b^2}\]

4) \(\large{(x-a)(x-b)=x^2-x(a+b)+ab}\)

\[\large{x(x-a)-a(x-b)=x(x)-x(a)-a(x)-a(-b)}\]
\[\large{x^2-ax-ax+ab}\]
\[\large{x^2-x(a+b)+ab=RHS}\]

.....

Answer 2

http://www.sosmath.com/tables/algiden/algiden.html

Answer 3

https://sites.google.com/site/tpiezas/001a