Mastering the Art of Simplifying Algebraic Expressions

When it comes to tackling the College Algebra CLEP exam, simplifying algebraic expressions is a fundamental skill you need in your toolkit. Let’s look at a simple yet effective example: simplifying ((x + 3)(x + 5)). You know what? Many who breeze through algebra forget just how pivotal this step can be. Getting it right can set the tone for the rest of your math problems.

So, how do we simplify ((x + 3)(x + 5))? First, we apply the Distributive Property — also known as the FOIL method for binomials, though I prefer to think of it as “focusing on the essential.” The Distributive Property is your best friend here; it helps break it down bit by bit.

When you expand ((x + 3)(x + 5)), it unfolds like this:

• First, multiply the first terms: (x \cdot x = x^2)
• Next, multiply the outer terms: (x \cdot 5 = 5x)
• Then, the inner terms: (3 \cdot x = 3x)
• Finally, multiply the last terms: (3 \cdot 5 = 15)

At this point, your expression looks like: [x^2 + 5x + 3x + 15]

Now, combine like terms — you’ll see that (5x + 3x) gives you (8x). So our simplified expression is: [x^2 + 8x + 15]

Now, let’s look at the choices as provided: A. (2x^2 + 8x + 15)
B. (x^2 + 8x + 15)
C. (2x^2 + 8x + 15)
D. (x^2 + 8x + 18)

It’s crucial to spot the subtle differences! The correct answer, as we found, is indeed B: (x^2 + 8x + 15).

Why are A and C wrong? They contain an additional term of (2x^2), which doesn’t fit our simplified version. It’s like ordering a burger but ending up with two! And D? It presents a constant of 18 instead of the correct 15. It’s all about attention to detail.

Here’s the thing — practice makes perfect. So, keep at it! Each time you grind through questions like these, you're sharpening your skills for the CLEP exam. You might even discover a few math tricks along the way; finding the right methods can transform complex problems into simple puzzles.

Remember, math isn’t just about numbers; it's about patterns and logic. So get comfortable with these kinds of problems, and you'll feel more confident walking into that exam room.

With determination and a sprinkle of smart studying, you’ll be able to simplify expressions and ace your College Algebra CLEP exam. Happy studying!