To multiply two polynomials, you apply the distributive property . Consider a simple example: multiplying a monomial by the binomial .
When you multiply one binomial by another binomial, you have to use the distributive property repeatedly.
There's a shortcut you can use here, known as the " FOIL " method (that stands for F irst, O uter, I nner, L ast.). The product of two binomials is the sum of four simpler products.
The product of the F irst terms is:
The product of the O uter terms is:
The product of the I nner terms is:
And the product of the L ast terms is:
Add all these up, and you'll get the answer:
You can use a similar strategy to multiply trinomials or other polynomials. For example, to multiply:
you need to find six products:
and then add them all up to get .