# Multiplying Monomials Monomials have only one term and therefore multiplying monomials is actually multiplying two terms.

## Step by step guide to multiplying monomials

• A monomial is a polynomial with just one term, like $$2x$$ or $$7y$$.
• To multiply monomials, first, we start by multiplying numbers (coefficients) and then multiplying unknowns (letters).
• Use the multiplication property of exponents to multiply exponents part of monomials. $$\color{blue}{x^a×x^b=x^{a+b}}$$

### Example 1:

Multiply expressions. $$-2xy^4 z^2×4x^2 y^5 z^3=$$

Solution:

Use multiplication property of exponents: $$\color{blue}{x^a×x^b=x^{a+b}}$$
$$x×x^2=x^{1+2}=x^3 , y^4×y^5=y^{4+5}=y^9$$ and $$z^2×z^3=z^{2+3}=z^5$$
Then: $$-2xy^4 z^2×4x^2 y^5 z^3=-8x^3 y^9 z^5$$

### Example 2:

Multiply expressions. $$-4a^4 b^3×5a^3 b^2=$$

Solution:

Multiplication property of exponents: $$\color{blue}{x^a×x^b=x^{a+b}}$$
$$a^4×a^3=a^{4+3}=a^7$$ and $$b^3×b^2=b^{3+2}=b^5$$
Then: $$-4a^4 b^3×5a^3 b^2=-20a^7 b^5$$

### Example 3:

Multiply expressions. $$5a^4 b^3×2a^3 b^2=$$

Solution:

Multiplication property of exponents: $$\color{blue}{x^a×x^b=x^{a+b}}$$
$$a^4×a^3=a^{4+3}=a^7$$ and $$b^3×b^2=b^{3+2}=b^5$$
Then: $$5a^4 b^3×2a^3 b^2=10a^7 b^5$$

### Example 4:

Multiply expressions. $$-4xy^4 z^2×3x^2 y^5 z^3=$$

Solution:

Multiplication property of exponents: $$\color{blue}{x^a×x^b=x^{a+b}}$$
$$x×x^2=x^{1+2}=x^3 , y^4×y^5=y^{4+5}=y^9$$ and $$z^2×z^3=z^{2+3}=z^5$$
Then: $$-4xy^4 z^2×3x^2 y^5 z^3=-12x^3 y^9 z^5$$

## Exercises

### Simplify each expression.

1. $$\color{blue}{2xy^2z × 4z^2}$$
2. $$\color{blue}{4xy × x^2y}$$
3. $$\color{blue}{4pq^3 × (– 2p^4q)}$$
4. $$\color{blue}{8s^4t^2 × st^5}$$
5. $$\color{blue}{12p^3 × (– 3p^4)}$$
6. $$\color{blue}{– 4p^2q^3r × 6pq^2r^3}$$

1. $$\color{blue}{8xy^2z^3}$$
2. $$\color{blue}{4x^3y^2}$$
3. $$\color{blue}{–8p^5q^4}$$
4. $$\color{blue}{8s^5t^7}$$
5. $$\color{blue}{–36p^7}$$
6. $$\color{blue}{–24p^3q^5r^4}$$ 30% OFF

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