OMTEX CLASSES: Algebraic Formulae

Algebraic Formulae

Algebra is one of the most basic part of mathematics , Algebra deals with variables and numbers.

Although Algebra is the basic mathematics , It deals with large numbers of formulas which relates two or more variables and numbers with each other.
To help you here is a list of Algebraic formulas.
Basic Algebraic Formulas:
The algebraic formulas involving basic relation between two and three variables are:
1>
a^2-b^2 = (a+b)\times (a-b)
2>
a^2+b^2 = (a+b)^2-2ab=(a-b)^2+2ab
3>
(a+b)^2 = a^2+2ab+b^2 = (a-b)^2+4ab
4>
(a-b)^2 = a^2-2ab+b^2 = (a+b)^2-4ab
5>
a^3+b^3 = (a+b) \times (a^2-ab+b^2) = (a+b)^3-3ab \times (a+b)
6>
a^3-b^3 = (a-b) \times (a^2+ab+b^2) = (a-b)^3+3ab \times (a-b)
7>
(a+b)^3 = a^3+3a^2b+3ab^2+b^3 = a^3+b^3+3ab \times (a+b)
8>
(a-b)^3 = a^3-3a^2b+3ab^2-b^3 = a^3-b^3-3ab \times (a+b)
9>
(x+a) \times (x+b) = x^2+x \times (a+b)+ab
10>
(x-a) \times (x+b) = x^2+x \times (b-a)-ab
11>
(x-a) \times (x-b) = x^2-x \times (a+b)+ab
12>
(a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ac
13>
(a+b+c)^3 = a^3+b^3+c^3+3(a+b)(b+c)(c+a)
14>
a^4-b^4 = (a-b) \times (a+b) \times (a^2+b^2)
15>
a^6-b^6 = (a+b) \times (a^2-ab+b^2) \times (a-b) \times (a^2+ab+b^2)
16>
a^6+b^6 = (a^2+b^2) \times (a^4-a^2b^2+b^4)
17>
a^4+a^2b^2+b^4 = (a^2-ab+b^2) \times (a^2+ab+b^2)
18>
(a-b-c)^2 = a^2+b^2+c^2-2ab+2bc-2ac
19>
a^3+b^3+c^3-3abc = (a+b+c) \times (a^2+b^2+c^2-ab-bc-ac)
Indices Formulas:
The formulas involving relations between variables and their powers or powers and indices are:
1>
x^m \times x^n = x^{m+n}
and
x^m \times x^n \times \ldots \times x^p = x^{m+n+ \ldots +p}
2>
x^m \div x^n = x^{m-n}
and
x^m \div x^n \div \ldots \div x^p = x^{m-n- \ldots -p}
3>
(x^m)^n = x^{m \times n}
and
((x^m)^n)^o) = x^{m \times n \times o}
4>
x^0 = 1
5>
x^{-m} = \dfrac{1}{x^m}
and
x^{m} = \dfrac{1}{x^{-m}}
6>
x^{\frac{m}{n}} = \sqrt[n]{x^m}
7>
\left( \dfrac{x^a}{y^b} \right)^c = \dfrac{x^{ac}}{y^{bc}}
8>
\dfrac{x^m}{y^m} = \left( \dfrac{x}{y} \right)^m
9>
\sqrt[m]{\dfrac{x^a}{y^b}} = \dfrac{x^{\frac{a}{m}}}{y^{\frac{b}{m}}}
10>
x^{\frac{p}{q}} = \sqrt[q]{x^p} = \left(\sqrt[q]{x}\right)^p
11>
\sqrt[m]{\dfrac{x}{y}} = \dfrac{\sqrt[m]{x}}{\sqrt[m]{y}}
12>
\sqrt{a} \times \sqrt {b} = \sqrt{a \times b}    provided that a , b and a*b are not negative numbers.
13>
If, a^x = a^y then , x=y. ( Provided That : 0 < a\text{ and }a \ne 1 )
14>
If, a^x = b^x then , a=b.  ( Provided That : 0 < a , b \text{ and }a , b \ne 1 )

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