Algebra is described as doing computations similar to those of arithmetic but with non-numerical mathematical symbols. These symbols are called variables.This method of representation helps in allowing the general formulation of arithmetic laws. It also provides a reference to unknown values providing access to find them out(by expressions and equations).
Here are some basic terms that are needed to be understood:
Variable: A variable is a letter that is used to represent unknown numbers.For example x,y,a,b,c,etc.
Constant: This is a fixed quantity that cannot be changed.
Algebraic Expression: It is a collation of variables and constants along with arithmetic operations. An Expression is made up of terms. Each expression should have at least one variable and one operation to be algebraic.
For example, in the algebraic expression 4x+3,
- x is variable
- 4 is the coefficient of x
- 3 is constant
- The above expression has two terms 4x and 3
Algebraic Equation: It is a mathematical statement with the equality symbol between two algebraic expressions.For example 3x+5=9,9x+3y+7=0,etc.
Here's a list of basic algebraic formulae for your reference:
a^2 – b^2 = (a – b)(a + b)
(a+b)^2 = a^2 + 2ab + b^2
a^2 + b^2 = (a – b)^2 + 2ab
(a – b)^2 = a^2 – 2ab + b^2
(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc
(a – b – c)^2 = a^2 + b^2 + c^2 – 2ab – 2ac + 2bc
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
(a – b)^3 = a^3 – 3a^2b + 3ab^2 – b^3
a^3 – b^3 = (a – b)(a^2 + ab + b^2 )
a^3 + b^3 = (a + b)(a^2 – ab + b^2 )
If n is a natural number, a^n – b^n = (a – b)(a^n-1 + a^n-2 b+…+ b^n-2 a + b^n-1 )
If n is even (n = 2k), a^n + b^n = (a + b)(a^n-1 – a^n-2 b +…+ b^n-2 a – b^n-1 )
If n is odd (n = 2k + 1), a^n + b^n = (a + b)(a^n-1 – a^n-2 b +…- b^n-2 a + b^n-1 )