Multiplying polynomials requires using the distributive property. This means that every term in one factor has to be multiplied by every term in the other factor. You may have learned the “FOIL” method for multiplying binomials. However, this method does not work quite so well for polynomials with terms greater than two.

First Outer Inner Last

Consider:

a). How would you use this same strategy to multiply the following?

\((2x+3)(4x^x-2x+5)\)

Remember that every term has to be multiplied by every other term. How do you know that each term has been multiplied by every other term?

b). Consider the trinomial you multiplied with the distributive property. \((x^2+2x – 1)(2x^2 – x + 1)\)

d). Explain how your would use the “FOIL” method to multiply the two trinomials.

e). Explain how FOIL is similar to the distributive property.