a.

Let’s break down the expression using the distributive property. When you multiply these two binomials, you’ll get:

Combine these results:

Reorganizing gives us:

And there you have it! This expression is now written in standard polynomial form.

Now, let’s put on our thinking caps! When you see a factored expression like this, think of it as a way to set the scene for quadratic solutions or graphing. The roots of the equation will show you the x-intercepts of the related parabola, allowing you to visualize its behavior on a graph.

Want to avoid common mistakes? When expanding, it’s easy to drop terms or miscalculate signs. A helpful tip is to ensure every term in the first binomial gets multiplied by every term in the second - a compact organization like the FOIL method (First, Outside, Inside, Last) can keep you on track. Double-checking your calculations at every stage can save you from potential headaches later on!