This document defines an algebraic identity and provides two examples. (1) An algebraic identity is an equality that holds true for all real numbers substituted for the variables. (2) The identity (x + y)u = xu + yu is demonstrated using rectangles with areas represented by the terms. (3) The identity (x+y)(u+v) = xu+xv+yu+yv is also demonstrated using rectangles.

2. IDENTITIES

3. If in two algebraic expressions which contain
letters, for all real numbers which settle instead
letters, they are equal to each other then, this
equality called Algebraic Identity.

4. ( x + y)u = xu + yu
x
u
y
A
CB C
F
E
Area of rectangle ABEF = xu
Area of rectangle ECDF = yu
Area of rectangle ABCD = Area of rectangle ABEF + Area of rectangle ECDF
Ie, (x + y)u = xu + yu
D

5. (x+y)(u+v) = xu+xv+yu+yv

6. xv yv
xu yu
B
C
A D
x y
u
v
Area of rectangle AGIE = xv
Area of rectangle GBFI = xu
Area of rectangle FCHI = yu
Area of rectangle EDHI = yv
Area of rectangle ABCD = Area of rectangle AGIE + Area of rectangle GBFI
+ Area of rectangle FCHI+Area of rectangle EDHI
Ie, (x + y)(u + v) =xu + xv + yu + yv
F
E
G H
I