what is algebra? and you give me a example

Algebra is a branch of mathematics that involves applying the rules of arithmetic to numbers and to letters that stand for unknown quantities. Letters, used to denote arbitrary unknown numbers and, numbers attached to the letters in the form of coefficients, state the relationship between the unkown quantities. (x + y)^2 = x^2 + 2xy + y^2 holds true for any two numbers x and y.