Multiplying Monomials Worksheet for 8th - 12th Grade | Lesson Planet - Free Printable

Problem Overview:

The task involves multiplying monomials and simplifying the results. Monomials are algebraic expressions consisting of a single term, such as $ 3x^2 $ or $ -5y^3 $. When multiplying monomials, we follow these rules:
1. Multiply the coefficients (numerical parts).
2. Add the exponents of like bases (variables).

We will solve each problem step by step.

---

Solutions:

#### Problem 1: $ 3x \cdot 4x $
- Multiply the coefficients: $ 3 \cdot 4 = 12 $.
- Add the exponents of $ x $: $ x^1 \cdot x^1 = x^{1+1} = x^2 $.
- Final answer: $ 12x^2 $.

#### Problem 2: $ 2x^2 \cdot 5x^3 $
- Multiply the coefficients: $ 2 \cdot 5 = 10 $.
- Add the exponents of $ x $: $ x^2 \cdot x^3 = x^{2+3} = x^5 $.
- Final answer: $ 10x^5 $.

#### Problem 3: $ 6x^3 \cdot 2x^4 $
- Multiply the coefficients: $ 6 \cdot 2 = 12 $.
- Add the exponents of $ x $: $ x^3 \cdot x^4 = x^{3+4} = x^7 $.
- Final answer: $ 12x^7 $.

#### Problem 4: $ 3x^2 \cdot 4x^3 $
- Multiply the coefficients: $ 3 \cdot 4 = 12 $.
- Add the exponents of $ x $: $ x^2 \cdot x^3 = x^{2+3} = x^5 $.
- Final answer: $ 12x^5 $.

#### Problem 5: $ 8x^3 \cdot 2x^2 $
- Multiply the coefficients: $ 8 \cdot 2 = 16 $.
- Add the exponents of $ x $: $ x^3 \cdot x^2 = x^{3+2} = x^5 $.
- Final answer: $ 16x^5 $.

#### Problem 6: $ 3x^2 \cdot 4x^3 $
- Multiply the coefficients: $ 3 \cdot 4 = 12 $.
- Add the exponents of $ x $: $ x^2 \cdot x^3 = x^{2+3} = x^5 $.
- Final answer: $ 12x^5 $.

#### Problem 7: $ 3x^2 \cdot 4x^3 $
- Multiply the coefficients: $ 3 \cdot 4 = 12 $.
- Add the exponents of $ x $: $ x^2 \cdot x^3 = x^{2+3} = x^5 $.
- Final answer: $ 12x^5 $.

#### Problem 8: $ 9x^2 \cdot 2x^3 $
- Multiply the coefficients: $ 9 \cdot 2 = 18 $.
- Add the exponents of $ x $: $ x^2 \cdot x^3 = x^{2+3} = x^5 $.
- Final answer: $ 18x^5 $.

#### Problem 9: $ 8x^3 \cdot 2x^2 $
- Multiply the coefficients: $ 8 \cdot 2 = 16 $.
- Add the exponents of $ x $: $ x^3 \cdot x^2 = x^{3+2} = x^5 $.
- Final answer: $ 16x^5 $.

#### Problem 10: $ 10x^2 \cdot 3x^3 $
- Multiply the coefficients: $ 10 \cdot 3 = 30 $.
- Add the exponents of $ x $: $ x^2 \cdot x^3 = x^{2+3} = x^5 $.
- Final answer: $ 30x^5 $.

#### Problem 11: $ 4x^2 \cdot 5x^3 $
- Multiply the coefficients: $ 4 \cdot 5 = 20 $.
- Add the exponents of $ x $: $ x^2 \cdot x^3 = x^{2+3} = x^5 $.
- Final answer: $ 20x^5 $.

#### Problem 12: $ 6x^2 \cdot 4x^3 $
- Multiply the coefficients: $ 6 \cdot 4 = 24 $.
- Add the exponents of $ x $: $ x^2 \cdot x^3 = x^{2+3} = x^5 $.
- Final answer: $ 24x^5 $.

#### Problem 13: $ 8x^3 \cdot 2x^2 $
- Multiply the coefficients: $ 8 \cdot 2 = 16 $.
- Add the exponents of $ x $: $ x^3 \cdot x^2 = x^{3+2} = x^5 $.
- Final answer: $ 16x^5 $.

#### Problem 14: $ 10x^2 \cdot 3x^3 $
- Multiply the coefficients: $ 10 \cdot 3 = 30 $.
- Add the exponents of $ x $: $ x^2 \cdot x^3 = x^{2+3} = x^5 $.
- Final answer: $ 30x^5 $.

#### Problem 15: $ 7x^2 \cdot 3x^3 $
- Multiply the coefficients: $ 7 \cdot 3 = 21 $.
- Add the exponents of $ x $: $ x^2 \cdot x^3 = x^{2+3} = x^5 $.
- Final answer: $ 21x^5 $.

#### Problem 16: $ 9x^2 \cdot 2x^3 $
- Multiply the coefficients: $ 9 \cdot 2 = 18 $.
- Add the exponents of $ x $: $ x^2 \cdot x^3 = x^{2+3} = x^5 $.
- Final answer: $ 18x^5 $.

#### Problem 17: $ 8x^3 \cdot 2x^2 $
- Multiply the coefficients: $ 8 \cdot 2 = 16 $.
- Add the exponents of $ x $: $ x^3 \cdot x^2 = x^{3+2} = x^5 $.
- Final answer: $ 16x^5 $.

#### Problem 18: $ 10x^2 \cdot 3x^3 $
- Multiply the coefficients: $ 10 \cdot 3 = 30 $.
- Add the exponents of $ x $: $ x^2 \cdot x^3 = x^{2+3} = x^5 $.
- Final answer: $ 30x^5 $.

#### Problem 19: $ 7x^2 \cdot 3x^3 $
- Multiply the coefficients: $ 7 \cdot 3 = 21 $.
- Add the exponents of $ x $: $ x^2 \cdot x^3 = x^{2+3} = x^5 $.
- Final answer: $ 21x^5 $.

#### Problem 20: $ 9x^2 \cdot 2x^3 $
- Multiply the coefficients: $ 9 \cdot 2 = 18 $.
- Add the exponents of $ x $: $ x^2 \cdot x^3 = x^{2+3} = x^5 $.
- Final answer: $ 18x^5 $.

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 12x^2 \\
2. & 10x^5 \\
3. & 12x^7 \\
4. & 12x^5 \\
5. & 16x^5 \\
6. & 12x^5 \\
7. & 12x^5 \\
8. & 18x^5 \\
9. & 16x^5 \\
10. & 30x^5 \\
11. & 20x^5 \\
12. & 24x^5 \\
13. & 16x^5 \\
14. & 30x^5 \\
15. & 21x^5 \\
16. & 18x^5 \\
17. & 16x^5 \\
18. & 30x^5 \\
19. & 21x^5 \\
20. & 18x^5 \\
\end{array}
}
\]