Mastering the Value of Expressions: A Guide to Understanding Algebraic Substitution

Algebra can sometimes feel like a puzzle, can’t it? Especially when you have to juggle variables and make sense of expressions. But don’t sweat it! Today, we’re diving into a specific example that shows just how valuable algebraic substitution can be—and trust me, it’s easier than it seems once you get the hang of it.

So, let’s break it down with an expression: 3y² - 2x + 4z. We’re given values for x, y, and z. In this case, we have (x=3), (y=-4), and (z=2). Your mission? Simplify this expression and find the answer. Ready? Let’s go!

First up, we take that y value of -4 and plug it straight into the 3y² term. It’s like a little math magic! You take (-4) and square it (which is (-4) times (-4) – that gives you 16), and then multiply it by 3. So you get:

• (3(-4)² = 3(16) = 48)

Now, isn’t that satisfying to see? Just wait, it gets even better!

Next, we tackle the x term. Remember, we're plugging in 3 into (-2x):

• (-2(3) = -6)

Now we’re rolling! We’ve got 48 from the first part and -6 from the second part. They’re coming together nicely.

Finally, let’s handle z. With our given z=2, we find the value for the term (4z):

• (4(2) = 8)

Now that all pieces are in place, it’s time to combine these results. You know what they say about math—everything works better together!

We take the 48 (from 3y²), subtract 6 (from -2x), and add 8 (from 4z):

• 48 - 6 + 8

Do you remember how to do this? Let’s break it down step-by-step:

1. First, (48 - 6 = 42).
2. Now, add in 8: (42 + 8 = 50).

And there you have it! The final value of the expression 3y² - 2x + 4z when (x=3), (y=-4), and (z=2) is 50.

What a rollercoaster ride, right? Each step is like unearthing a clue in a mystery novel, leading you to the grand reveal at the end. Plus, mastering these techniques can really boost your confidence in tackling similar algebra problems, especially when you’re preparing for tests that assess your math skills.

So, as you prepare for your upcoming Accuplacer test, remember that practicing substitution and understanding algebraic expressions like this will not only help you with that exam but will also make you feel like a math wizard. And who wouldn’t want that kind of power, right?