Given two polynomials, their can be calculated by using the . Consider, for example, the following pair of polynomials.
To multiply these two polynomials, the following four steps can be followed.
Distribute One Polynomial to All the Terms of the Other
Start by writing the product P(x)⋅Q(x).
Next, distribute P(x)
to each term of Q(x).
Clear Parenthesis by Applying the Distributive Property
Apply the Distributive Property one more time to clear all the parentheses.
Apply the Product of Powers Property
Using the to rewrite some products as one single power.
Combine Like Terms and Simplify
Finally, and perform all the required to simplify the result.
Note that multiplying a polynomial with
by a polynomial with
products. Also, when two polynomials are multiplied, the product is a new polynomial whose equals the of the degrees of the multiplied polynomials.
Two polynomials can also be multiplied using the Box Method and the , however, the latter is useful only for multiplying binomials. Keep in mind that these two methods are based on the Distributive Property.