algebraic formulas

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In the algebraic formula sheets we have all algebraic formulas which are used in solving algebraic expressions. Algebra is a major part of mathematics, in algebra we includes all relations and operations. Algebraic formulas are used in quadratic equations, binomial theorems, difference of squares, law of exponents etc. Following is the list of some important Algebraic Formulas that we use in solving the Algebraic expression.

1.    (a+b) ^2 = a^2 + 2ab + b^2

2.    (a-b) ^2 = a^2 -2ab + b^2

3.    (a + b) ^3 = a^3 + 3a^2b + 3ab^2 + b^3

4.    (a – b) ^3 = a^3 – 3a^2b + 3ab^2 – b^3

5.    a^3 – b^3 = (a – b) (a^2 + ab + b^2)

6.    a^3 + b^3 = (a + b) (a^2 – ab + b^2)

7.    x^m . x^n = x^ (m+n)

8.    x^m / x^n = x^(m – n)

9.    (x^m) ^n = x^mn

10. (xy) ^m = x^m y^m)

Following are the some examples based on the algebraic formulas
 
Example 1: - Solve given expression x^2 – 49

Solution: - Given equation is:-

x^2 – 49

ð  (x+7) (x-7) [ As a^2 – b^2 = (a+b) (a-b)]

Hence x^2 – 49 = (x+7) (x-7)

Example 2:  Solve given expression b^2 (a^4) ^2 / a^6

Solution:- Given equation is

b^2 (a^4) ^2 / a^6

In order to solve these types of questions we have to use law of exponents.

= b^2 a^8/a^6

= b^2 a^ (8-6)

= b^2 a^2

Hence the solution for the algebraic expression b^2 (a^4)^2 / a^6  is b^2 a^2.
 
 
 
 

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