Print This Page
**Multiplication Of A Monomial And A Polynomial**: At a Glance

- Topics At a Glance
- Exponents
- Negative Exponents
- Fractional Exponents
- Irrational Exponents
- Variables as Exponents
- Defining Polynomials
- Degrees of a Polynomial
- Multivariable Polynomials
- Degrees of Multivariable Polynomials
- Special Kinds of Polynomials
- Evaluating Polynomials
- Roots of a Polynomial
- Combining Polynomials
**Multiplying Polynomials****Multiplication of a Monomial and a Polynomial**- Multiplication of Two Binomials
- Special Cases of Binomial Multiplication
- General Multiplication of Polynomials
- We'll Divide Polynomials Later!
- Factoring Polynomials
- The Greatest Common Factor
- Recognizing Products
- Trial and Error
- Factoring by Grouping
- Summary
- Introduction to Polynomial Equations
- Solving Polynomial Equations
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

The easiest case of polynomial multiplication is multiplying a monomial and a polynomial. In this case, we "distribute" the monomial to each term in the polynomial. We really do distribute it, though. We weren't using the quotation marks to be sarcastic or ironic.

What is (2*x*)(3*x*^{2} + 4*x* + 9) ?

We use the distributive property to distribute (2*x*) over the longer polynomial, then simplify the resulting terms.

(2x)(3x^{2} + 4x + 9) | = | (2x)(3x^{2}) + (2x)(4x) + (2x)(9) |

= | 6x^{3} + 8x^{2} + 18 |

What is (5*x*^{2})(4*x*^{3} + 7*x*)?

We distribute (5*x*^{2}) to find (5*x*^{2})(4*x*^{3}) + (5*x*^{2})(7*x*),

which simplifies to 20*x*^{5} + 35*x*^{3}.

Example 1

Find (2y)( |

Exercise 1

Find the product of (4*x*)(x + 11).

Exercise 2

Find the product of (2*x*^{3})(*x*^{3} + 3*x*^{2} + 4*x* + 9).

Exercise 3

Find the product of (-*x*^{2})(2*x*^{4} - 11*x* + 17).

Exercise 4

Find the product of (4*x*)(*x*^{2} + xy + 3y^{2}).

Exercise 5

Find the product of (0)(14*x*^{23} + 6*x*^{17} - 8*x*^{9} + 14).