# Polynomials - Long Multiplication

A polynomial looks like this:

example of a polynomial this one has 3 terms |

We can multiply small polynomials using the method shown on Multiplying Polynomials

But when the polynomials have 3 or more terms it is often easier (and less likely to have a mistake) when we use a method similar to Long Multiplication for Numbers (please read that page first).

## The Method

Choose one polynomial (the longest is a good choice) and then:

- multiply it by
**the first term**of the other polynomial, writing the result down - then multiply it by
**the second term**of the other polynomial, writing the result under the matching terms from the first multiplication - then multiply it by
**the third term**of the other polynomial (if any) etc ... - lastly, add up the columns.

Laying the work out neatly in columns is the key, like this:

*(I wrote column headings of x, x ^{2} and x^{3}, but you don't have to)*

By **lining up the columns**, and being careful to **put the terms under the correct columns**, the job becomes "automatic", and we can easily look back to see if we got it right, too.

But what happens if a polynomial is missing, say, an **x** term or an **x ^{2}** term? Just leave that column blank!

Here is a more complicated example, with blank gaps:

## More than One Variable

So far we have been multiplying polynomials with only one variable (**x**), but how do we handle polynomials with two or more variables (such as **x** and **y**)? What are the column headings?

Just ignore the columns in the question, write down the answers as they come, **always checking** to see if we could put an answer under a matching answer: