Detemine Multiplying a Polynomial by a Monomial?

To multiply a polynomial by a monomial, use the distributive property.

Let's start by talking about ordinary numbers. Say that you want add two numbers (a and b) together, and multiply the sum by a third number (c). by c. With ordinary numbers, you would most likely add a and b first, then multiply the sum
The expression would look like this: c (a + b).

However, you can get the same result in another way, by multiplying c times a, then c times b, and adding the products:
(cxa)+ (cxb) = c(a+b)

The distributive property allows us to perform this operation on monomials and polynomials, as well as on ordinary numbers.
Let's see how it works:

Example 1: Evaluate 2(x + 4).

2(x + 4)
= 2(x) + 2(4)
=2x + 8

Example 2: Evaluate 3(y - 5).

3(y - 5)
= 3(y) - 3(5)
=3y - 15

Example 3: Evaluate 3x(y2 + 2x - 5).

3x(y2 + 2x - 5)
= 3x(y2) + 3x(2x) -3x(5)
= 3xy2 + 6x2 - 15x