Subtracting Polynomials

Steps for adding polynomials:

1. Remove the brackets

2. Combine the like terms

Example

(5x² + 7x - 9) + (-3x² - 5x + 2)

1. Drop the brackets
5x² + 7x - 9 -3x² - 5x + 2

2. Combine like terms

Example cont.

5x² + 7x - 9 - 3x² - 5x + 2

= 2x² + 2x - 7

Try these examples about adding polynomials

Subtracting polynomials is the same as adding polynomials, but with one extra step

Extra step: Change the minus to a plus, and change the second bracket to its opposite.

The opposite is when we change the signs of a term from plus to minus, or minus to plus
For example, the opposite of 5 is: -5
The opposite of 2x + 9 is: -2x - 9

What is the opposite?

Step 1: Change the minus to a plus and change the second bracket to the opposite
Step 2: Drop the brackets
Step 3: Combine like terms

(3x + 7) - (x - 2)

Step 1: Change the minus to a plus, and the second bracket to its opposite
(3x + 7) + (-x + 2)

(3x + 7) + (-x + 2)

Step 2: Drop the brackets

3x + 7 - x + 2

Step 3: Combine like terms

3x + 7 - x + 2

= 2x + 9

So, (3x + 7) - (x - 2) = 2x + 9

(4a² - 3a - 1) - (6a² - 5a + 3)

Step 1: Change minus to plus, change second bracket to opposite

(4a² - 3a - 1) + (-6a² + 5a - 3)

Step 2: Drop brackets
Step 3: Combine Like Terms

4a² - 3a - 1 - 6a² + 5a - 3

= -2a² + 2a - 4

Try these examples about subtracting polynomials. You have 2 mins for each one. Use paper and pencil or a whiteboard to help!