Mathematics Algebras

ADDITION OF ALGEBRAIC EXPRESSION                      Like terms only addition  Example:           1)  Find the total number of apples?                     5 apples + 6 apples = 11 apples                         2) Find the total number of fruits?                          5 apples + 6 oranges = 11 fruits             3x+4x= 7x           5y+8y= 13y                6z+ 9z= 15z               3x^2 +5x^2= 8x^2 Unlike terms  not added            3x+4y            5a+ 7b           8y+ 9z     ...

DEFINITION OF ALGEBRAIC EXPRESSION IN ADDITION              *     A terms  is a part of an expressions that  are add or subtracted                *    5x+6-4x                 *   This expressions has 3 terms : 5x ,6, and 4x.             *   A like terms  are terms  who have  the same variable raised to the same power.             *  In the  expression  above. 5x and 4x are like terms 

DEFINITION OF ALGEBRAIC EXPRESSION                     In mathematics, an algebraic expressions is an expressions  built up from  integer constants , variables and the algebraic  operation ( addition , subtraction,  Multiplication,  division and exponentiation  by an exponent that is a rational number)                 For example :            3x^2-2xy+c is an algebraic expression    

NUMBER OF TERMS AND CO-EFFICIENT EXAMPLES: Numbers of terms:                    2ab+3a^b -7 ----> 3 terms                   5xy+3y.          -----> 2terms                    3xyz.             ------> 1 terms                   8xy+6zx+7y+6  -----‐> 4terms Coefficient  :                3xyz  in coefficient - 3               2ab+ 3a^2b-7a in coefficient- 2,3,-7               5xy + 7ab+ 89 in coefficient  - 5,7,89               3a + 26 a^2 -5ca^2 in coefficient - 3, 26, 5               2x+ 6y+ 9x-2y in coefficient  - 2,6,9, -2

NUMBER OF TERMS  AND  CO-EFFICIENT            A  term is a single  mathematics expression.            It may be a single number ( positive or  negative), a singl variable ( a letter), serveral variable  multiplied but never added or subtracted. Some terms contain variable with a number in front of them. The number in front of a term is called a coefficient. 

UNLIKE TERMS                    x^2 ,  3y , 3a^2 ,4x,  5x^2 , y , 9p^2 , 46a^2 , 9ab , 5z.     Unlike  Terms:                    x^2, 3y , 3a^2 , 4x , 9p^2 , 9ab ,5z

LIKE TERMS                      x^2 , 3y , 3a^2b^2 , 4x ,6x^2 , 9p^2 ,  -6y , 46a^2 , 9ab, -25x ,- 5x^2 ,2x, -8p^2,  5a^2b^2, 4ab    Like terms               i)   x^2 ,6x^2 , -5x^2             ii)  3y, -6y             iii) 9p^2 , -8p^2            iv) 9ab, 4ab            v) 3a^2b^2 , 5a^2b^2           vi) 4x,  2x, -25x

 ALGEBRAIC OF EXPRESSIONS         2x, 4x, 6x, 8a, 5b, 4y, 8x,9t,5k , x, 5t , 7s , PATTERN                  1, 2 , 3 , 4 ,............n^th         2 , 4 , 6 , 8 ,............n^th         3 , 6 , 9 ,12,.............n^th        4, 8 ,12, 16,..............n^th       5, 10,15, 20, ............n^th       6, 12, 18, 24, ...........n^th

CONSTANT AND VARIABLE  CONSTANT             1,2,3,4,5,...............       VARIABLE               a,b,c,d,e,...............      Examples:          i)    2x+5             x=1 , 2(1)+5 = 2 +5 = 7         x=2 , 2(2)+5 = 4 +5 = 9        x=3 , 2(3)+5 = 6 +5 =11                  ii)    5y+8                 y=1 , 5(1)+8 = 5 +8 = 13         y=2 , 5(2)+8 = 10+8=18         y=3 , 5(3)+8 =15+8 =23          iii)   6a+5b             a=1 , b=1                6(1)+5(1) = 6+5= 11          a=2, b=2     6(2)+ 5(1...

BASIC CONCEPTS OF ALGEBRA Constant,  Variable  Like terms Unlike term Coefficient  Algebra Expression    Addition Subtraction 

MEANING OF ALGEBRAIC           Algebra from Arabic                     Al-jabr       MEANING: Réunion of broken parts and                                bonesetting   

Introduction to Algebra 1) Finding the number of things to its cost. 2) Expressing the distance covered in terms of speed and time.  3) Converting miles into kilo metters, grams to kilograms etc. 4)Finding the length of the barbed wire to fence a garden.  5) Finding the areas of a park  6)Finding the missing numbers in a sequence.