Simplifying Expressions: Understanding Polynomial Operations

When it comes to algebra, particularly during the Accuplacer test, understanding polynomial operations can feel like a daunting task. But fear not! We're breaking down the expression 5y(2y - 3) + (2y - 3) so that you can tackle similar problems with confidence and ease.

Let’s start from the top. Why do we care about simplifying expressions like this one? Well, knowing how to manipulate polynomials not only helps you answer math questions correctly but also strengthens your overall problem-solving skills. And who wouldn’t want to feel like a math whiz?

Alright, the expression we’re working with is 5y(2y - 3) + (2y - 3). First things first! It’s important to notice the common structure in both terms — you can see that (2y - 3) appears twice. This gives us a big clue: we can factor that out! But before we dive into factoring, let’s distribute and expand the expression to begin simplifying it.

Here’s the thing: when you distribute 5y to each term inside the parentheses (2y - 3), you get:

• 5y * 2y = 10y²
• 5y * -3 = -15y

Now, bring down the other term from the expression, (2y - 3):

10y² - 15y + 2y - 3.

Hang tight—this is where it gets fun! Now it's time to combine like terms. Combining -15y and 2y gives us -13y. So, we now have:

10y² - 13y - 3.

Woohoo! You’ve simplified the expression like a champ. At this point, you might be wondering what to do next. Here’s where options A through D come in, but let’s keep it real. Our simplified version is equivalent to the correct choice: (5y + 1)(2y - 3).

Why does this matter? Understanding these connections is part of mastering algebra. It’s like building a puzzle; once you find the right pieces, everything clicks into place. Plus, being able to manipulate polynomials helps in a variety of applications, from geometry to calculus!

So, what can you take away from this? First and foremost, don’t shy away from practicing problems like this. As with anything, repetition breeds familiarity. Try breaking down other expressions using the same techniques — distribute, combine like terms, and look for common factors. You’ll start noticing patterns, and soon enough, algebra coefficients and variables will become second nature to you.

If you’ve made it this far, give yourself a pat on the back! You’re on your way to mastering polynomial expressions and ready to tackle the Accuplacer test with confidence. Just remember, math isn’t a monster waiting to pounce; it's a set of tools you can wield to solve real-world problems. So keep practicing, and soon, you’ll feel right at home simplifying expressions like a pro!