Question

Algebraic idenrities important rules in calculation

Answer 1

Algebra Identities

Difference of Squaresa2 - b2 = (a-b)(a+b)

Difference of Cubesa3 - b3 = (a - b)(a2+ ab + b2)

Sum of Cubesa3 + 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 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 termd 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 factorr 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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