Basic Information on Algebra

Introduction for basic information on algebra:

Algebra is the division of mathematics connecting to the study of the regulations of operations and associations, and the organization and ideas occurrence from them, jointly with terms, polynomials, equations and algebraic structures. Collectively with geometry, examination, topology, combinatory, and number theory, algebra is one of the mainly significant divisions of pure mathematics.

Some Basic Information of Algebra:

The following information is very useful for basic algebra.

1. Make a revision of the basic formula with deference to the signs:

(plus +)    +  (plus +)    =   (plus+ )
(minus -)  +  (minus- )  =   (minus -)
(plus +)    *   (plus +)    =   (plus+ )
(minus -)  *   (minus- )  =   (plus +)
(minus -)  *   (plus + )   =   (minus -)
(plus +)    *   (minus- )  =   (minus -)


2. Practicing with the basic formulas:

(x + y) 2 =x2 + y2 + 2xy.
(x - y) 2 =x2 + y2 – 2xy.
x 2 – y 2 = (x + y) (x - y).


3. Attempt the quadratic equation with regard to x and y and solve correspondingly

Example Problems for Basic Information on Algebra:

Example 1 for basic information on algebra:

1) (s + 4) (s – 5)

Solution:

= (s + 4) (s – 5)

= s2 -5s + 4s– 20

= s2 - 1s- 20

Example 2 for basic information on algebra:

2) Solve this algebra expression: 5(a -3) + 4b - 5(a -b -3) + 12

Solution:-

Using Multiply Factors

= 5a - 15 + 4b -5a + 5b + 15 + 12

Groups like terms

= 9b + 12

Example 3 for basic information on algebra:

3) Using algebra equation solve: 3(-5x - 2) - (x - 2) = -2(8x + 4) + 4

Solution:-

Multiplying factors:

-15x – 6 - x + 2 = -16 x - 8 + 4

Group like terms:

-16x – 4 = -16x – 4

Add 16x + 4  to both sides and using the equations as fallows

0 = 0

Example 4 for basic information on algebra:

4) Calculate the value of the following algebra problem: `103^2`

Solution:

Given 1032

= (100+3)2

= 1002+ 2(100) (3) + 32

= 10000 + 600 + 9

= 10609.