# At a Glance - Multiplication of a Monomial and a Polynomial

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.

### Sample Problem

What is (2x)(3x2 + 4x + 9)?

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

 (2x)(3x2 + 4x + 9) = (2x)(3x2) + (2x)(4x) + (2x)(9) = 6x3 + 8x2 + 18x

### Sample Problem

What is (5x2)(4x3 + 7x)?

We distribute (5x2) over both terms in the second set of parentheses, then simplify.

(5x2)(4x3) + (5x2)(7x) =
20x5 + 35x3

#### Example 1

 What is (2y)(x2 + 3xy – y)?

#### Exercise 1

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

#### Exercise 2

Find the product of (2x3)(x3 + 3x2 + 4x + 9).

#### Exercise 3

Find the product of (-x2)(2x4 – 11x + 17).

#### Exercise 4

Find the product of (4x)(x2 + xy + 3y2).

#### Exercise 5

Find the product of (0)(14x23 + 6x17 – 8x9 + 14).