9/26-9/28 – Distributive Property of Stuff

The main idea is that two entire polynomials can be multiplied with the distributive property. Example:

Find the product of x + 3 and x - 5

Instead of distributing a single term, we can distributive an entire polynomial. Whoa! In this problem, we can distribute the x - 5:

(x+3)\textbf{(x - 5)} = x\textbf{(x - 5)} + 3\textbf{(x - 5)}

Let’s reflect on what just went down. The entire (x-5) polynomial was distributed to the “x” in (x+3) and then to the “3” in (x + 3).

OK, now what? We are going to use the distributive property again!

x\textbf{(x - 5)} + 3\textbf{(x - 5)} = x(x) + x(-5) + 3(x) + 3(-5) = x^2-5x+3x-15 = x^2 - 2x - 15

Maybe you’ll encounter some people who try to teach this topic using all sorts of tips and tricks. That’s OK. But never lose sight of the fact that multiplying polynomials is nothing other than the distributive property!

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