Algebra Formula: Definition, Formulas and Examples

Algebra Formula

Algebra Identities

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 Expansions

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 ab and c are the leading coefficients.

The roots for this quadratic equation will be:

roots of quadratic equation

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:

Algebra

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:

sum of the first n term, Sn = [a(1-r^n)]/[1-r]

The sum to infinity

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

Sum to infinity, a/(1-r)

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