Mastering College Math: Your Simplification Guide

What is the simplified form of the expression 4x(2y) + 3y(2−x)?

• A. 5xy + 6y
• B. 8xy + 6y − x
• C. 11xy + 6y
• D. 8xy + 6y − 3x

Answer: (A)

To simplify the expression 4x(2y) + 3y(2−x), we start by distributing the terms in each part of the expression. First, look at the term 4x(2y). When simplifying this, we multiply 4x by 2y, which gives us: 4x(2y) = 8xy. Next, we simplify the term 3y(2 - x). Here, we distribute 3y across both terms within the parentheses: 3y(2) - 3y(x) = 6y - 3xy. Now, we can combine the simplified results from both parts of the expression: 8xy + (6y - 3xy). When combining like terms, specifically the xy terms, we notice that: 8xy - 3xy = 5xy. Putting everything together gives us: 5xy + 6y. This matches option A perfectly. By breaking down the expression carefully and combining like terms, we see that the correct simplification leads us to the answer of 5xy + 6y.

When preparing for the College Math Placement Test, knowing how to simplify algebraic expressions can really boost your confidence. Let's unravel a particular expression together, shall we? Consider the expression: 4x(2y) + 3y(2−x). It sounds a bit daunting, but trust me, it’s simpler than it seems!

First, what’s the first step when faced with an expression like this? Yes, distributing those terms! It's a bit like spreading butter on warm toast—take your time and get it just right. Let’s start with 4x(2y). If you multiply 4x by 2y, you'll find yourself with 8xy.

Now, onto the next part: 3y(2−x). Here, we apply what we know about distribution. You’ll multiply 3y by both parts inside the parentheses. So, you’ll end up with 3y times 2 and 3y times -x, giving us 6y and -3xy, respectively. When we piece together these results, it’s like assembling a jigsaw puzzle—it’s satisfying to see it come together: 8xy + 6y - 3xy.

Now, we find ourselves at a critical juncture: combining like terms. Look closely at 8xy and -3xy. If you take 3 away from 8, how much do you have left? That’s right—5xy! So now we can compile everything into one neat expression: 5xy + 6y.

It’s amazing how breaking things down makes the whole process more manageable, don’t you think? It’s like tackling a big project one small piece at a time. This final form, 5xy + 6y, corresponds perfectly to option A from our original question.

As you gear up for your placement test, remember this process: distribute, combine, and simplify. Each step you master adds to your toolkit, making you just that much more ready to tackle whatever math comes your way. And who knows, you might even find it pretty rewarding—and enjoyable, because math doesn’t have to be scary!

The journey through simplification doesn’t just end here. Think of it as a skill you'll take with you into higher-level math courses and beyond. Embrace it, practice it, and watch how it pays off in all sorts of academic situations. Happy studying!