OPERATIONS IN ALGEBRAIC EXPRESSION

ADDITION AND SUBTRACTION

Example : Addition or subtraction of algebraic expressions

 Simplify each of the following :

 a)         7x + 4 – 2x + 6

 b)         s + s² – 5 + 4 + 2s

 c)         3mn + 6 – 4nm – 3

Solution :

a)                    7x + 4 – 2x + 6          

=         7x – 2x + 4 + 6

=         5x + 10

                        b)                    s + s² – 5 + 4 + 2s

=         s + 2s - 5 + 4  + s²

=         3s – 1 + s²

=         s² + 3s – 1

c)                    3mn + 6 – 4nm – 3

=         3mn – 4mn  +  6 – 3

=         -mn + 3

MULTIPLICATION AND DIVISION

 Example : Multiplication of algebraic expressions

 Multiply each of the following expression :  

a)            4a x 5b

b)            2ab x 3bc²

Solution :

a)            4a x 5b =  4 x a  x  5 x b

 =  4 x 5  x  a x b

 =  20 x ab

 =  20ab

b)        2ab x 3bc² =  2 x a x b  x  3 x b x c x c

      =  2 x 3  x  a x b x b x c x c

      =  6 x ab²c²

      =  6ab²c²

Example : Division of algebraic expressions

 Solve the following problems :

a)            6ab²c³ ¸ 2bc²

b)            10m²n³ ¸ 5mn3p

c)            4s x 7t ¸ s²

REMOVAL OF BRACKETS

The rules of removing brackets are as follows :

  + (a + b )   =   a + b

  + (a - b )    =   a - b

  - (a + b )    = -a + b

  - (a - b )     = -a - b

Example : Removing brackets of algebraic expressions

Simplify : 

a)            (a + 3b) – (2a + b)

b)            -(3x – 2xy) + ( x – 2xy)

Solution :

a)                            (a + 3b) – (2a + b)

=         a + 3b – 2a – b

=         a – 2a + 3b – b

=         -a + 2b

b)                            -(3x – 2xy) + ( x – 2xy)

=         -3x + 2xy + x – 2xy

=         2xy – 2xy - 3x + x

=         -2x