# How to Multiply a Polynomial and a Monomial? (+FREE Worksheet!)

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.

\(\color{blue}{a×(b+c)=a×b+a×c} \)

**The Absolute Best Books to Ace Pre-Algebra to Algebra II**

### 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: \(\color{blue}{a \ (b \ + \ c)=ab \ + \ ac} \)

Then: \( -4x(5x+9)=-20x^2-36x \)

**The Best Book to Help You Ace Pre-Algebra**

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

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

**Solution:**

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

Then: \(2x(6x^2-3y^2 )=12x^3-6xy^2\)

## 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

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

**The Greatest Books for Students** **to Ace the Algebra**

## Related to This Article

### More math articles

- 7th Grade MEA Math Worksheets: FREE & Printable
- 8th Grade PSSA Math FREE Sample Practice Questions
- How to Use Number Lines for Multiplication by a Negative Integer?
- The Ultimate ILTS Elementary Education Math (Grades 1–6) (305) Course
- Perimeters and Areas of Rectangles
- How to Factor Polynomials?
- Algebra Puzzle – Challenge 42
- How to Factor Quadratics Using Algebra Tiles
- Discovering the Magic of Triangle Midsegments
- 8th Grade SC Ready Math Worksheets: FREE & Printable

## What people say about "How to Multiply a Polynomial and a Monomial? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.