Author: Kathy Halverson
Last saved by: Glencoe Mathematics
Company: Halverson Household

Lesson 13-3

Example 1	Subtract Polynomials
Find each difference.
a.	(7x + 8) – (2x + 3)

    7x + 8
(-)2x + 3		Align like terms.
          5x + 5		Subtract.

b.	(2b^2 + 4b – 7) – (6b^2 + 3)

	2b^2 + 4b  - 7
(-)  6b^2          + 3	Align like terms. 
           -4b^2 + 4b – 10	Subtract.		

Example 2	Subtract Using the Additive Inverse
Find each difference.
a.	(5x + 2) – (3x + 4)
The additive inverse of 3x + 4 is (-1)(3x + 4) or –3x – 4.

(5x + 2) – (3x + 4)
    = (5x + 2) + (-3x – 4)	To subtract (3x + 4), add (–3x – 4).
    = (5x + -3x) + (2 + -4)	Group the like terms.
    = 2x – 2	Simplify.

b.	(3x^3 + 2x^2y^2 + 7y^2) – (5x^3 – 6xy + 9y^2)
The additive inverse of 5x^3 – 6xy + 9y^2 is (-1)( 5x^3 – 6xy + 9y^2) or -5x^3 + 6xy - 9y^2.

3x^3 + 2x^2y^2               + 7y^2	      3x^3 + 2x^2y^2               + 7y^2
(-)  5x^3                    – 6xy  + 9y^2	→	(+) -5x^3                   + 6xy – 9y^2	Align the like terms and
	    -2x^3 + 2x^2y^2 + 6xy – 2y^2	add the additive inverse.

Example 3	Subtract Polynomials to Solve a Problem
PRODUCTION The cost of producing x units is 750 + 2.5x. The revenue earned from the sale of x units is 14.5x. Write an expression for the profit earned when producing and selling x units. Remember, profit = revenue – cost.

profit = revenue – cost	Formula for profit
= 14.5x – (750 + 2.5x)	Substitution.
= 14.5x + (-750 – 2.5x)	Add the additive inverse.
= [14.5x + (-2.5x)] + (-750)	Group like terms.
= 12x – 750	Simplify.
The profit for producing and selling x items can be expressed by 12x – 750.