Adding and subtracting polynomials coloring worksheet answer key

Learn how to add and subtract polynomials and how to combine like terms and simplify polynomials in this article.

Related Topics

• How to Multiply Monomials
• How to Multiply and Dividing Monomials
• How to Multiply Binomials
• How to Factor Trinomials
• How to Write Polynomials in Standard Form

Step by step guide to solve adding and subtracting polynomials

• Adding polynomials is just a matter of combining like terms, with some order of operations considerations thrown in.
• Be careful with the minus signs, and don’t confuse addition and multiplication!

Adding and Subtracting Polynomials – Example 1:

Simplify the expressions. \((2x^3-4x^4 )-(2x^4-6x^3 )=\)

Solution:

First use Distributive Property for \(-(2x^4-6x^3 )= -2x^4+6x^3 \)
\((2x^3-4x^4 )-(2x^4-6x^3 )=2x^3-4x^4-2x^4+6x^3 \)
Find “like” terms and combine them: \(2x^3+6x^3=8x^3\), \(-4x^4-2x^4=-6x^4\)

Now simplify: \(2x^3-4x^4-2x^4+6x^3=-6x^4+8x^3\)

Adding and Subtracting Polynomials – Example 2:

Add expressions. \((x^3-2)+(5x^3-3x^2 )=\)

Solution:

Remove parentheses: \((x^3-2)+(5x^3-3x^2 )=x^3-2+5x^3-3x^2\)
Combine like terms: \(x^3+5x^3=6x^3\)

Now simplify: \(x^3-2+5x^3-3x^2=6x^3-3x^2-2\)

Adding and Subtracting Polynomials – Example 3:

Subtract. \((4x^3+3x^4 )-(x^4-5x^3 )=\)

Solution:

First use Distributive Property for \(-(x^4-5x^3 )=-x^4+5x^3 \)
\( (4x^3+3x^4 )-(x^4-5x^3 )=4x^3+3x^4-x^4+5x^3 \)
Combine like terms: \(4x^3+5x^3=9x^3\), \(3x^4-x^4=2x^4\)

Now simplify: \(4x^3+3x^4-x^4+5x^3=2x^4+9x^3\)

Adding and Subtracting Polynomials – Example 4:

Add expressions. \((2x^3-6)+(9x^3-4x^2 )=\)

Solution:

Remove parentheses: \((2x^3-6)+(9x^3-4x^2 )=2x^3-6+9x^3-4x^2\)
Combine like terms: \(2x^3+9x^3=11x^3\)

Now simplify: \(2x^3-6+9x^3-4x^2=11x^3-4x^2-6\)

Exercises for Adding and Subtracting Polynomials

Simplify each expression.

1. \(\color{blue}{(2x^3 – 2) + (2x^3 + 2)}\)
2. \(\color{blue}{(4x^3 + 5) – (7 – 2x^3)}\)
3. \(\color{blue}{(4x^2 + 2x^3) – (2x^3 + 5)}\)
4. \(\color{blue}{(4x^2 – x) + (3x – 5x^2)}\)
5. \(\color{blue}{(7x + 9) – (3x + 9)}\)
6. \(\color{blue}{(4x^4 – 2x) – (6x – 2x^4)}\)

Download Adding and Subtracting Polynomials Worksheet

1. \(\color{blue}{4x^3 }\)
2. \(\color{blue}{6x^3 – 2}\)
3. \(\color{blue}{4x^2 – 5}\)
4. \(\color{blue}{– x^2 + 2x}\)
5. \(\color{blue}{4x}\)
6. \(\color{blue}{6x^4 – 8x}\)

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10 months ago

With this activity, students will add and subtract polynomials. They will then identify the coefficient of a specific term or constant of the simplified expression and color it accordingly to complete a beautiful pattern! As an added bonus, the final product makes fabulous classroom decor!

This activity is an excellent resource for sub plans, enrichment/reinforcement, early finishers, and extra practice with some fun. It is especially useful for end-of-year practice, spiral review, and motivated practice when students are exhausted from standardized testing or mentally “checked out” before a long break (hello summer!). Teachers and students alike enjoy motivating activities, so engage your students today with this fun color by number activity!

Name__________________________________________________Date_______________________________________

Adding and Subtracting Polynomials Color by Number Directions: Add or subtract each polynomial below. Then color the picture according to the indicated coefficient or constant of your solution. Show your work on a separate sheet of paper.

Expression

Simplified Expression

1. (5𝑝2 − 3) + (2𝑝2 − 3𝑝3 ) 2.

(𝑎3

− 2𝑎

2)

2

3

− (3𝑎 − 4𝑎 )

Use the coefficient of this term

Color

𝑝2

Yellow

𝑎

3

Redorange

constant

Navy blue

𝑛3

Light blue

constant

Black

𝑟3

Plum

constant

Gray

8. (−4𝑘 4 + 14 + 3𝑘 2 ) + (−3𝑘 4 − 14𝑘 2 − 8)

𝑘2

Yellow

9. (3 − 6𝑛5 − 8𝑛4 ) − (−6𝑛4 − 3𝑛 − 8𝑛5 )

𝑛5

Redorange

3. (4 + 2𝑛3 ) + (5𝑛3 + 2) 4. (4𝑛 − 3𝑛3 ) − (3𝑛3 + 4𝑛) 5. (3𝑎2 + 1) − (4 + 2𝑎2 ) 6. (4𝑟 3 + 3𝑟 4 ) − (𝑟 4 − 5𝑟 3 ) 7. (5𝑎 + 4) − (5𝑎 + 3)

10. (12𝑎5 − 6𝑎 − 10𝑎3 ) − (10𝑎 − 2𝑎5 − 14𝑎4 ) 11. (8𝑛 − 3𝑛 + 10𝑛 4

2)

2

4

− (3𝑛 + 11𝑛 − 7)

12. (9𝑟 3 + 5𝑟 2 + 11𝑟) + (−2𝑟 3 + 9𝑟 − 8𝑟 2 )

𝑎

5

Navy blue

𝑛

Light blue

𝑟

Black

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