Multiplying Polynomials

Hello mathematicians, puzzlers, and other curious people!

Multiplying ordinary numbers is easier than lots of other things once you\’ve got the hang of it (though getting the hang of it in the first place can be tricky), but multiplying more complicated expressions can be — well, more complicated.

Here\’s one example: what if you need to multiply by ?

OK, that wasn\’t too bad! It\’s really just a distributive property problem.

But, what happens if we have two polynomials, and neither one of them is a monomial? For example, what if we want to know about times ?

As you can see, even though the distributive property is still the property of mathematics we\’re relying on to get through polynomial multiplication, we can use a little geometric logic to make the process easier. I\’ve had so many students miss some combinations of one term from the first polynomial and another from the second, when they use other methods with long polynomials, but when using the box method it\’s easy to see if you skipped anything because there\’ll be an empty space.

What are some other kinds of algebraic expressions that you might try to multiply? The comments section is open for brainstorming and talking it over.

Calc You Later!