Mastering the PERT: Product of Binomials Explained

When it comes to preparing for the Postsecondary Education Readiness Test (PERT), getting a grip on algebra is key. Whether you're feeling a bit rusty on your binomials or you're just looking for practice, you’ve landed in the right place. Let’s tackle the product of the expression ((2m - 5n)(4m + n)), breaking it down using a method you probably learned in math class: the FOIL method.

FOIL? What’s That Again?
FOIL stands for First, Outer, Inner, Last, a handy mnemonic that helps you remember the order in which you need to multiply terms in two binomials. Kind of like trying to remember the directions to your favorite coffee shop — once you get the hang of it, it becomes second nature!

First Things First: Let’s Multiply the First Terms
With our problem ((2m - 5n)(4m + n)), we'll start with the "First" step. Multiply the first terms from each binomial:
[
2m \cdot 4m = 8m^2
]
So far, so good, right? That's the foundation we’ll build on.

What’s on the Outside?
Next, we hit the "Outer" terms:
[
2m \cdot n = 2mn
]
Keep this in mind — we'll be seeing it again in a bit!

Now, the Inner Workings
Then comes the "Inner" terms. Don’t underestimate this step. Multiply:
[
-5n \cdot 4m = -20mn
]
That’s right, another term with (mn). Now you might be wondering, “Wait, isn't that a bit of a mouthful?” Yes, indeed!

A Touch of the Last
Finally, let’s finish strong with the "Last" terms:
[
-5n \cdot n = -5n^2
]
Now we can combine all these lovely results, but we’re not done yet.

Combining Our Results
Put it all together:
[
8m^2 + 2mn - 20mn - 5n^2
]
Now, let’s group the like terms, which means we need to combine (2mn) and (-20mn):
[
8m^2 - 18mn - 5n^2
]
And there it is—the simplified expression we were aiming for.

When prepping for the PERT and similar tests, it’s essential to be comfortable with these kinds of problems. Think of this like building a toolbox for your academic journey. Each skill you gain—whether it’s multiplying binomials or solving quadratic equations—is like adding another tool to your arsenal. And remember, don’t shy away from practicing these. Practice might make perfect, but it definitely builds confidence!

Feel free to revisit this article as a study guide or reference as you progress. Each problem solved is a step closer to dominating the PERT. You've got this; now, go ace that test!