Introduction

Adding polynomials involves combining like terms.

Subtracting Polynomials

To subtract polynomials, remember to distribute the – sign into all the terms in the parenthesis.

At the end of the lesson, the students should be able to:

• Identify the adding and subtracting polynomials
• Perform the adding and subtracting polynomials
Process

Step 1: Arrange each polynomial with the term with the highest degree first then in decreasing order of degree.

Step 2: Group the like terms. Like terms are terms whose variables and exponents are the same.

Step 3: Simplify by combining like terms.

Sample Problem:

Add the polynomials. (2x² + 6x +5) + ( 3x²– 2x – 1)

Step 1: The polynomials are in decreasing order of degree.

Step 2: Group the like terms.

2x² + 3x² + 6x – 2x + 5 -1

Step 3: Simplify by combining the like terms

2x² + 3x² + 6x – 2x + 5 -1

5x²+ 4x + 4

Example:

Add the polynomials 5x – 2 + y and –3y + 5x + 2

Solution:

5x – 2 + y + (–3y + 5x + 2)

= 5x + 5x + y – 3y – 2 + 2

= 10x – 2y

Example:

Find the sum of –7x³y + 4x²y² – 2 and 4x³y + 1 – 8x²y²

Solution:

–7x³y + 4x²y²– 2 + 4x³y + 1 – 8x²y²

= –7x³y + 4x³y + 4x²y²– 8x²y² – 2 + 1

= –3x³y – 4x²y² – 1

Steps to Subtract Polynomials:

To subtract Polynomials, first reverse the sign of each term we are subtracting (turn “+” into “-“, and “-“ into “+”), then follow the previous steps to add polynomials.

Sample Problem:

Subtract the polynomials.

5y² + 2xy – 9 – (2y² +2xy – 3)

Step 1: Reverse the sign of each term we are subtracting.

5y² + 2xy – 9 - (2y² + 2xy – 3)

5y² + 2xy – 9 + (-2y² - 2xy + 3)

Step 2: The polynomials are in decreasing order of degree.

Step 3: Group the like terms.

5y² – 2y² +2xy – 2xy – 9 + 3

Step 4: Simplify by combining the like terms.

5y² – 2y² +2xy – 2xy – 9 + 3

3y² – 6

Example:

Simplify –4x + 7 – (5x – 3)

Solution:

–4x + 7 – (5x – 3)

= –4x + 7 – 5x + 3

= –9x + 10

Example:

Simplify (5x² + 2) – (– 4x² + 7) + (– 3x² – 5)

Solution:

(5x² + 2) – (– 4x² + 7) + (– 3x²– 5)

= 5x² + 2 + 4x²– 7 – 3x²– 5

= 5x² + 4x²– 3x² + 2 – 7 – 5

= 6x² – 10

Examples of adding and subtracting polynomials

1. (4x² - 3x + 2) + (5x² + 2x - 7)

2. (5x³ + 7x² - x) + (8x³ + 4x - 5)

3. (8x² + 2x) - (10x² + 2x - 9)

4 -(6x³ - 4x) - (2x³ + x² -2x)

Evaluation

Perform the operations.

1.(12y²+ 17y - 4) + (9y²- 13y + 3) =

2.(2x³+ 7x² + x) + (2x²- 4x - 12) =

3.(-3m² + m) + (4m²+ 6m) =

4.(7z³+ 4z - 1) + (2z²- 6z + 2) =

5.(3a²+ 2a - 2) - (a² - 3a + 7) =

6.(5x²- 2x - 1) - (3x²- 5x + 7) =

7.-(3z² + 4z) - (6z²- 2) =

8.(6x³- 4x²+ x - 9) - (3x² + 7x + 3) =

9.(2x²+ 1) + (x²- 2x + 1) =

10.(-s²- 3) - (2s² + 10s) =

Conclusion