Algebra Formula
Algebra Identities
Difference of Squares

a^{2} – b^{2} = (ab)(a+b)
Difference of Cubes

a^{3} – b^{3} = (a – b)(a^{2}+ ab + b^{2})
Sum of Cubes

a^{3} + b^{3} = (a + b)(a^{2} – ab + b^{2})
Special Algebra Expansions
Formula for (a+b)^{2} and (ab)^{2}

(a + b)^{2} = a^{2} + 2ab + b^{2}

(a – b)^{2} = a^{2} – 2ab +b^{2}
Formula for (a+b)^{3} and (ab)^{3}

(a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}

(a – b)^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3}
Roots of Quadratic Equation
Formula
Consider this quadratic equation:

ax^{2} + bx + c = 0
Where a, b and c are the leading coefficients.
The roots for this quadratic equation will be:
Arithmetic Progression
Arithmetic progression
Consider the following arithmetic progression:

a + (a + d) + (a + 2d) + (a + 3d) + …
Where:

a is the initial term

d is the common difference
The n^{th} term
The n^{th} term, T_{n} of the arithmetic progression is:

T_{n} = a + (n – 1)d
Sum of the first n term
The sum of the first n terms of the arithmetic progression is:
Geometric Progression
Geometric progression
Consider the following geometric progression:

a + ar + ar^{2} + ar^{3} + …
Where:

a is the scale factor

r is the common ratio
The n^{th} term
The n^{th} term, T_{n} of the geometric progression is:

T_{n} = ar ^{n – 1}