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.

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

### Download Multiplying Monomials Worksheet

- \(\color{blue}{8xy^2z^3}\)
- \(\color{blue}{4x^3y^2}\)
- \(\color{blue}{–8p^5q^4}\)
- \(\color{blue}{8s^5t^7}\)
- \(\color{blue}{–36p^7}\)
- \(\color{blue}{–24p^3q^5r^4}\)