WEEK 3 (EXPRESSIONS)

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ALGEBRA (WEEK 3)

Kind of Expression

1.     Monomial expression

A term in which its variables have positive integers exponent

Example:   2x², 3xyz,  4x²y²z,  3x²/2

Not monomial:    2x^-2   1/x³    xy^-2z,  2√x

2.     Polynomial expression

An expression with two or more terms

A combination of monomials using addition and subtraction

Examples:   2x + 1,  2x² – y,  x +  2y – 3z,    4x²y + 4xy – 3y

Not polynomials:    2x + y^-1,   1/y – 1/x ,   y^-1 / x + 1,   2x + √y

2.1  Binomial expression – polynomial with two terms

       2x + y,    5x² – 3,    x² + 2y²

2.2 Trinomial expression – polynomial with three terms

      4x² + 3y² – 3,    x² – 2x + 3

3.     Rational Expression

An expression in the form of  p/r

 Where p and r are polynomials

Example:

4.     Radical Expression

Expression in the form of   

   where n Is an integer and p is a polynomial

Example:

ADDING AND SUBTRACTING EXPRESSION

Similar terms:  two or more term with the same literal coefficient

Example:

2x,  5x,  -4x

2x²y, 14x²y,  -4x²y

12xy,  10yx,  -3 xy

9xyz, 3xzy,  4yx

Rules in adding or subtracting terms

1.     Only similar terms can be added

2.     Add or subtract the numerical coefficient of similar term

3.     Attached the common literal coefficient

Example 1.

            3xy + 5xy   (similar term)

            Add the numerical coefficient:    3 + 5  = 8

            Then attach the common literal coefficient :  8xy

Example 2:

          4xyz   + 3mno   -2xyz   + mno  

 Add the similar term:

     Similar term are   4xyz  and  - 2xyz,      3mno and mno

            4-2   = 2, then attach the common literal coefficient    2xyz

             3 + 1 = 4, then attach the common literal coefficient   4mno

            Answer is    2xyz + 4mno

Note: you cannot add dissimilar term:

            X + y = cannot be added, so answer is x + y

            Y + 1 = cannot be added, so answer is  y + 1

            x + 2x + y = 3x + y

Adding and subtracting Expression:

Addition

1.     Add 2x² – 2x + 3 and 5x² -3x + 5

SSOLUTION:

(2x² – 2x + 3) + (5x² -3x + 5)

simplify

=  2x² – 2x + 3 + 5x² -3x + 5

Combine all similar term

=  2x²+ 5x²– 2x  -3x + 5 + 3

Add similar term

= 7x² – 5x + 8

2^nd method (row method)  

2x² – 2x + 3

5x² -3x + 5

7x² – 5x + 8

2.     Add:     3x³–3x²–4x–3  ,   2x³ – 2x + 2 and  –x³ –2x² +4x -5

            By row method

                  Note:    Line up expression,only similar term can be line up in the same row. Then add each row

                        3x³ –3x² –4x–3 

2x³         – 2x + 2

–x³ –2x² +4x –5

4 x³–4 x²– 2x – 6

SUBTRACTION OF EXPRESSION:

1.     (2x² – 2x + 3)   –  (x² + 4x – 5)

Step 1, simplify by using distributive method:

            2x² – 2x + 3   –  x² – 4x + 5  Note:  (–  ) should be distributed to all member of expression in subtrahend

Step 2. Combine all similar term then add,

                              2x² –  x² – 2x  – 4x + 3   + 5 

                        =    x² – 6x  + 8

            2^nd Method: Row method

                                                Change the sign of all subtrahend, then add

      2x² – 2x + 3                               2x² – 2x + 3

x² + 4x – 5       -------->              –x² – 4x + 5

                                                x² – 6x  + 8

Example 2:

            Subtract  4x³ – 3x² – 2x + 5  from  6x³ – 2x² + 5x– 2

Solution:

             6x³ – 2x² + 5x– 2                        6x³ – 2x² + 5x– 2

                    -  4x³ – 3x² – 2x + 5        -------->  +  –4x³+3x²  +2x – 5 

                                                                         2 x³ + x² + 7x– 7