Math Formula

Algebra Formula


Difference of Squares

  • a2 - b2 = (a-b)(a+b)

Difference of Cubes

  • a3 - b3 = (a - b)(a2+ ab + b2)

Sum of Cubes

  • a3 + b3 = (a + b)(a2 - ab + b2)

Special Algebra Formula


Formula for (a+b)2 and (a-b)2

  • (a + b)2 = a2 + 2ab + b2
  • (a - b)2 = a2 - 2ab +b2

Formula for (a+b)3 and (a-b)3

  • (a + b)3 = a3 + 3a2b + 3ab2 + b3
  • (a - b)3 = a3 - 3a2b + 3ab2 - b3

Roots of Quadratic Equation


Formula

Consider this quadratic equation:
  • ax2 + 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 nth term

The nth term, Tn of the arithmetic progression is:
  • Tn = 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 + ar2 + ar3 + ...
Where:
  • a is the scale factor
  • r is the common ratio

The nth term

The nth term, Tn of the geometric progression is:
  • Tn = ar n - 1

Sum of the first n terms

The sum of the first n terms, Sn is:
  •  

The sum to infinity

If -1 < r < 1, the sum to infinity, S∞ is:
  •  


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