In one of the articles, we learnt about adding and subtracting polynomials. In this post, we will learn about multiplying polynomials. We will start from very basic polynomials to make this lesson effective and easy for you.

Let's suppose that we want to multiply and . We can note that both of the polynomials have a single term.

where

In such a case, we just need to use one of the laws of exponents. ().

So, if we have and to multiply then answer would be equal to .

Take another example now, we want to multiply by . What would be the answer?

. Exponents of variables and are added whereas variable was present in just one term.

Now let's cover some typical examples. If, we want to multiple one polynomial with the sum of two polynomials. What do we do?

Ist polynomial (2nd Polynomial + 3rd Polynomial)

= (Ist polynomial 2nd polynomial) + (Ist polynomial 3rd polynomial)

Let's suppose we want to multiply by .

. We cannot further simply this because exponents of and are different.

Problems can be made more complex. We can have problems of the form:

(Ist polynomial + 2nd polynomial) (3rd polynomial + 4th polynomial)

= (Ist polynomial 3rd polynomial) + (Ist polynomial 4th polynomial)

+ (2nd polynomial 3rd polynomial) + (2nd polynomial 4th polynomial).

Now take one example. We want to multiply by

.

We cannot simplify it further because no terms can be added in the last step.