II. POLYNOMIAL ARITHMETIC

We add polynomials by combining similar terms (like terms).

Example: Add 6a + b , -5ab - b, 2a + 3ab, and 6b

Solution:

6a + b + (-5ab) + (-b) + 2a + 3ab + 6b

= 6a + 2a + b + (-b) + 6b + (-5ab) + 3ab

= 8a + 6b - 3ab

Subtraction often requires the use of parenthesis.

Example: Subtract -3xy + 7xyz from 2xy - 3yz + 7xz

Solution:

2xy - 3yz + 7xz - (-3xy + 7xyz)

= 2xy - 3yz + 7xz + 3xy - 7xyz

= 2xy + 3xy - 3yz + 7xz - 7xyz

= 5xy - 3yz + 7xz - 7xyz

When working with Parenthesis , Brackets and Braces it is important to remember the order of operations and to work from the inner most parenthesis out.

EX: Simplify: 3{ 5 [(-2a + (-3b)² - 1) - 2(a - b) + 5(1 - 2b)] }

Solution:

3{ 5 [(-2a + (-3b)² - 1) - 2(a - b) + 5(1 - 2b)] }

= 3{ 5 [ -2a + 9b² - 1 - 2a + 2b + 5 - 10b ] }

= 3{ 5 [ 9b² - 4a - 8b + 4 ] }

= 3{ 45b² - 20a - 40b + 20 }

= 135b² - 60a - 120b + 60
 
 
 
 

The Distributive law is used in the multiplication of polynomials .

Example: Find the product of 3ab and a² + ab + 2c

Solution: 3ab(a² + ab + 2c) = 3a³b + 3a²b² + 6abc
 
 

The FOIL distribution method described on page 34 of Module VII is used when multiplying one binomial by another binomial .

Example: Find the product of 2x + 5 and 2x - 5