Adding and Subtracting Polynomials

Introduction

Adding Polynomials

Adding polynomials involves combining like terms.

Subtracting Polynomials

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

Task

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

Steps to Add Polynomials:

To add polynomials we simply add any like terms together.

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

Adding And Subtracting Polynomials

Adding polynomials and subtracting polynomials is essentially combining like terms of polynomial expressions. When adding and subtracting polynomials, they can either be arranged vertically or grouped according to degree. A knowledge of polynomial vocabulary is important before adding and subtracting polynomials. Multiplying monomials and binomials is another type of operation with polynomials.

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