Basic Algebra - Distributive Law - Expanding and Simplifying

Hello and Welcome! In this video, I'm going to demonstrate how to expand and simplify a basic algebraic expression.

And the expression that we are given here is...

(3 - 2x)(3x + 1)

Now, to first expand this expression we have to apply what is called the "distributive law" of algebra. And that basically states how we should multiply through.

We multiply each element in the first bracket with each element in the second bracket to get the complete expression.

So the first thing we going to do is to multiply 3 x 3x, and then we're going to multiply 3 x 1. And then subsequently, we have to multiply -2x x 3x and then the -2x x 1.

When I was at high school my maths teacher at the time called this the "moon method" because we have a shape here that looks a bit like a crescent moon!

So let's evaluate this expansion. We have...

(3 - 2x)(3x + 1) = 3·3x + 3·1 - 2x·3x + 2x·1

= 9x + 3 - 6x² + 2x

= 11x + 3 - 6x²

That's how you would expand and simplify a common, basic algebraic expression. If you have any math questions please comment below and I'll endeavor to answer them in future videos.