Subtracting Polynomials

Subtracting Polynomials

Review: Adding 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

YOU TRY

Try these examples about adding polynomials

Fill in the Blanks

Write your answer with no spaces.

(4x + 5y) + (6x + 7y)

Fill in the Blanks

Write your answer with no spaces.

(5a - 3b + 2c) + (4a + 5b - 7c)

Subtracting 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.

What is the 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

YOU TRY

What is the opposite?

Fill in the Blanks

What is the opposite of 6?

Fill in the Blanks

What is the opposite of -5?

Fill in the Blanks

What is the opposite of 2x?

Fill in the Blanks

What is the opposite of x - 9?

(Write your answer with no spaces)

Multiple Choice

What is the opposite of -2x² - 3x - 1

• -2x² + 3x + 1

• 2x² + 3x + 1

• 2x² - 3x + 1

• 2x² + 3x - 1

Multiple Choice

What is the opposite of 2m + 3n - 5

• -2m -3n + 5

• 2m -3n + 5

• -2m +3n + 5

• -2m -3n - 5

Steps for subtracting polynomials

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

Example

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

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

Example

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

Step 2: Drop the brackets

3x + 7 - x + 2

Step 3: Combine like terms

Example

3x + 7 - x + 2

= 2x + 9

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

Another Example

(4a² - 3a - 1) - (6a² - 5a + 3)

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

Another Example

(4a² - 3a - 1) + (-6a² + 5a - 3)

Step 2: Drop brackets
Step 3: Combine Like Terms

Another Example

4a² - 3a - 1 - 6a² + 5a - 3

= -2a² + 2a - 4

YOU TRY

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

Multiple Choice

(7x - 3y) - (4x + 2y)

• 3x - 5y

• 3x - y

• 3x + y

• 3x + 5y

Multiple Choice

(8a - 2b) - (6a + 3b)

• 2a - b

• 2a + b

• 2a - 5b

• 2a + 5b

Multiple Choice

(6x² - 2) - (3x² + 5)

• 3x² - 3

• 3x² + 3

• 3x² + 7

• 3x² - 7

Multiple Choice

(5x - y) - (6x - 7y)

• -x + 6y

• -x - 6y

• x + 6y

• x - 6y

Multiple Choice

(-4a - 3b) - (6a - 5b)

• 2a + 2b

• 2a - 2b

• -10a + 2b

• -10a - 2b

Multiple Choice

(-3x - 3y -4) - (-7x - 5y - 2)

• 4x - 2y - 6

• 4x + 2y - 2

• -10x - 8y - 6

• -10x + 8y - 2

Fill in the Blanks

Write your answer with no spaces

(5x + 7y) - (2x + 4y)

Fill in the Blanks

Write your answer with no spaces

(3a + 4b - 7c) - (a - 7b + 3c)

Poll

How are you feeling about today's lesson?

• I didn't get anything!

• I'm still confused. I have questions

• I feel so-so. I understand a few things

• I get it. I am feeling good.

• I get it completely! I feel like an expert!