Learn how to multiply monomials to polynomials using the distributive property and the multiplication property of exponents.

## Related Topics

- How to Multiply Monomials
- How to Multiply and Dividing Monomials
- How to Multiply Binomials
- How to Factor Trinomials
- How to Add and Subtract Polynomials

## Step by step guide to Multiplying a Polynomial and a Monomial

- When multiplying monomials, use the product rule for exponents.
- When multiplying a monomial by a polynomial, use the distributive property.

\(\color{blue}{a×(b+c)=a×b+a×c} \)

### Multiplying a Polynomial and a Monomial – Example 1:

Multiply expressions. \(2x(-2x+4)=\)

**Solution:**

Use Distributive Property: \(\color{blue}{a \ (b \ + \ c)=ab \ + \ ac} \)

Then: \(2x(-2x+4)=-4x^2+8x \)

### Multiplying a Polynomial and a Monomial – Example 2:

Multiply expressions. \(-2x(3x^2+4y^2 )=\)

**Solution:**

Use Distributive Property: \(\color{blue}{a \ (b \ + \ c)=ab \ + \ ac} \)

Then: \(-2x(3x^2+4y^2 )=-6x^3-8xy^2\)

### Multiplying a Polynomial and a Monomial – Example 3:

Multiply expressions. \(-4x(5x+9)=\)

**Solution:**

Use Distributive Property: \( -4x(5x+9)=-20x^2-36x \)

### Multiplying a Polynomial and a Monomial – Example 4:

Multiply expressions. \(2x(6x^2-3y^2 )=\)

**Solution:**

Use Distributive Property: \(2x(6x^2-3y^2 )=12x^3-6xy^2\)

## Exercises for Multiplying a Polynomial and a Monomial

### Find each product.

- \(\color{blue}{5 (3x – 6y)}\)
- \(\color{ blue }{9x (2x + 4y)}\)
- \(\color{blue}{8x (7x – 4)}\)
- \(\color{blue}{12x (3x + 9)}\)
- \(\color{blue}{11x (2x – 11y)}\)
- \(\color{blue}{2x (6x – 6y)}\)

### Download Multiplying a Polynomial and a Monomial Worksheet

- \(\color{blue}{15x – 30y}\)
- \(\color{blue}{18x^2 + 36xy}\)
- \(\color{blue}{56x^2 – 32x}\)
- \(\color{blue}{36x^2 + 108x}\)
- \(\color{blue}{22x^2 – 121xy}\)
- \(\color{blue}{12x^2 – 12xy}\)