Multiplying Monomials worksheets - Free Printable

Sure! Let’s solve each problem step by step. The task is to multiply monomials — that means multiplying the coefficients (numbers) and adding the exponents of like variables.

---

General Rule:

When multiplying monomials:
- Multiply the coefficients (numbers).
- For each variable, add the exponents if the base is the same.
- Keep variables that appear in only one monomial.

---

Let’s go through each problem:

---

1) $-9x^2y^3z \times 5x$

- Coefficients: $-9 \times 5 = -45$
- $x^2 \times x = x^{2+1} = x^3$
- $y^3$ stays (no other y)
- $z$ stays

✔ Answer: $-45x^3y^3z$

---

2) $9xy \times 4x^2y$

- Coefficients: $9 \times 4 = 36$
- $x \times x^2 = x^{1+2} = x^3$
- $y \times y = y^{1+1} = y^2$

✔ Answer: $36x^3y^2$

---

3) $-4xy \times (-2z)$

- Coefficients: $-4 \times -2 = 8$
- $x$ stays
- $y$ stays
- $z$ stays

✔ Answer: $8xyz$

---

4) $8x^2y^3z \times 5x$

- Coefficients: $8 \times 5 = 40$
- $x^2 \times x = x^3$
- $y^3$ stays
- $z$ stays

✔ Answer: $40x^3y^3z$

---

5) $5x^2y^3z \times 4x$

- Coefficients: $5 \times 4 = 20$
- $x^2 \times x = x^3$
- $y^3$ stays
- $z$ stays

✔ Answer: $20x^3y^3z$

---

6) $2x^2y^2z \times 2xz^2$

- Coefficients: $2 \times 2 = 4$
- $x^2 \times x = x^3$
- $y^2$ stays
- $z \times z^2 = z^3$

✔ Answer: $4x^3y^2z^3$

---

7) $-5xy \times (-3z)$

- Coefficients: $-5 \times -3 = 15$
- $x$ stays
- $y$ stays
- $z$ stays

✔ Answer: $15xyz$

---

8) $-8x^2y^2z \times 7xz^2$

- Coefficients: $-8 \times 7 = -56$
- $x^2 \times x = x^3$
- $y^2$ stays
- $z \times z^2 = z^3$

✔ Answer: $-56x^3y^2z^3$

---

9) $9x^2y^2z \times 5xz^2$

- Coefficients: $9 \times 5 = 45$
- $x^2 \times x = x^3$
- $y^2$ stays
- $z \times z^2 = z^3$

✔ Answer: $45x^3y^2z^3$

---

10) $5xy \times 2x^2y$

- Coefficients: $5 \times 2 = 10$
- $x \times x^2 = x^3$
- $y \times y = y^2$

✔ Answer: $10x^3y^2$

---

11) $-6x^2y^2z \times 7xz^2$

- Coefficients: $-6 \times 7 = -42$
- $x^2 \times x = x^3$
- $y^2$ stays
- $z \times z^2 = z^3$

✔ Answer: $-42x^3y^2z^3$

---

12) $2xy \times 4x^2y$

- Coefficients: $2 \times 4 = 8$
- $x \times x^2 = x^3$
- $y \times y = y^2$

✔ Answer: $8x^3y^2$

---

13) $-3x^2y^2z \times 4xz^2$

- Coefficients: $-3 \times 4 = -12$
- $x^2 \times x = x^3$
- $y^2$ stays
- $z \times z^2 = z^3$

✔ Answer: $-12x^3y^2z^3$

---

14) $7xy \times 2x^2y$

- Coefficients: $7 \times 2 = 14$
- $x \times x^2 = x^3$
- $y \times y = y^2$

✔ Answer: $14x^3y^2$

---

15) $-1xy \times 3x^2y$

- Coefficients: $-1 \times 3 = -3$
- $x \times x^2 = x^3$
- $y \times y = y^2$

✔ Answer: $-3x^3y^2$

---

16) $-10x^2y^2z \times 4xz^2$

- Coefficients: $-10 \times 4 = -40$
- $x^2 \times x = x^3$
- $y^2$ stays
- $z \times z^2 = z^3$

✔ Answer: $-40x^3y^2z^3$

---

17) $-8xy \times (-3z)$

- Coefficients: $-8 \times -3 = 24$
- $x$ stays
- $y$ stays
- $z$ stays

✔ Answer: $24xyz$

---

18) $2x^2y^3z \times 3x$

- Coefficients: $2 \times 3 = 6$
- $x^2 \times x = x^3$
- $y^3$ stays
- $z$ stays

✔ Answer: $6x^3y^3z$

---

19) $-5xy \times 4x^2y$

- Coefficients: $-5 \times 4 = -20$
- $x \times x^2 = x^3$
- $y \times y = y^2$

✔ Answer: $-20x^3y^2$

---

20) $-5x^2y^2z \times 5xz^2$

- Coefficients: $-5 \times 5 = -25$
- $x^2 \times x = x^3$
- $y^2$ stays
- $z \times z^2 = z^3$

✔ Answer: $-25x^3y^2z^3$

---

21) $8x^2y^2z \times 7xz^2$

- Coefficients: $8 \times 7 = 56$
- $x^2 \times x = x^3$
- $y^2$ stays
- $z \times z^2 = z^3$

✔ Answer: $56x^3y^2z^3$

---

22) $3x^2y^3z \times 3x$

- Coefficients: $3 \times 3 = 9$
- $x^2 \times x = x^3$
- $y^3$ stays
- $z$ stays

✔ Answer: $9x^3y^3z$

---

## ✔ Final Answers List:

1) $-45x^3y^3z$
2) $36x^3y^2$
3) $8xyz$
4) $40x^3y^3z$
5) $20x^3y^3z$
6) $4x^3y^2z^3$
7) $15xyz$
8) $-56x^3y^2z^3$
9) $45x^3y^2z^3$
10) $10x^3y^2$
11) $-42x^3y^2z^3$
12) $8x^3y^2$
13) $-12x^3y^2z^3$
14) $14x^3y^2$
15) $-3x^3y^2$
16) $-40x^3y^2z^3$
17) $24xyz$
18) $6x^3y^3z$
19) $-20x^3y^2$
20) $-25x^3y^2z^3$
21) $56x^3y^2z^3$
22) $9x^3y^3z$

---

Let me know if you want a printable version or explanations for specific problems!