Multiply Polynomials

A big part of converting quadratic equations from one form to another is the ability to multiply polynomials. A polynomial is a fancy term that describes an algebraic expression of 2 or more terms. For instance, 2x + 3 and 4xy + 3x + 5 are polynomials of 2 and 3 terms, respectively. We’ll begin by multiply two binomials.

You can find the product of two binomials by multiplying each term in the first binomial by each term in the second binomial. If necessary, simplify by collecting like-terms at the end.

The method we used above can be summarized as FOIL, which stands for FIRST-OUTER-INNER-LAST. Teachers and students often refer to this technique as FOILing.

Let’s a take a look at this technique in action.

When we multiplying binomials, there are some interesting patterns to note. If you forget them, it won’t hinder your ability to multiply, just as long you know how to expand. Nonetheless, it’s good to recognize them:

When squaring a binomial, you add the two equal middle terms after expansion:

  • (a + b)² = a² + 2ab + b²
  • (a – b)² = a² – 2ab + b²

When you multiply the sum and the difference of two terms, the two middle terms are opposites, so they add to zero.

  • (a + b)(a – b) = a² – b²

Now, what if we have more complicated polynomials being multiplied? Let’s take a look at other examples you may come across.