What is the rule for adding and subtracting algebraic terms?

Cracking the Code: Adding and Subtracting in Algebra (It’s Easier Than You Think!)

So, you’re diving into algebra? Awesome! One of the first things you’ll need to nail down is how to simplify expressions. And guess what? It all boils down to one golden rule: you can only add or subtract what are called “like terms.”

“Like terms?” What’s all that about, you ask? Simple. They’re terms that share the same variable – that’s the letter, like ‘x’ or ‘y’ – and that variable has to be raised to the same power. Think of it like this: you can’t add apples and oranges, right? Same idea here.

Let’s break down a term, piece by piece, just to be crystal clear:

• Coefficient: This is the number hanging out in front of the variable. In something like 5x, the ‘5’ is the coefficient.
• Variable: The letter itself, like ‘x’, ‘y’, or even ‘z’. It represents some unknown value we’re trying to figure out.
• Exponent: That little number floating up in the air next to the variable (like the ‘2’ in 5×2). It tells you what power the variable is raised to. If you don’t see an exponent, it’s automatically a ‘1’. So, ‘x’ is the same as ‘x1’.

Okay, back to our golden rule. Let’s say you’ve got this expression: 3x + 2y + 5x – y. Can we tidy it up? You bet!

Spot the like terms:

• 3x and 5x are buddies because they both have ‘x’ to the power of 1.
• 2y and -y are also pals – they both rock the ‘y’ to the power of 1.

Now, let’s combine them:

• 3x + 5x? That’s 8x. Easy peasy.
• 2y – y? Remember that if there’s no number in front of the ‘y’, it’s like there’s a sneaky ‘1’ hiding there. So, 2y – 1y = y.

That means our simplified expression is: 8x + y. And that’s as far as we can go! We can’t mush those two together because they’re not like terms. They’re different things entirely.

Why all the fuss about “like terms only?” Well, it’s because algebra is built on solid logic. You can easily add up a bunch of the same thing, but you can’t directly combine different things. It’s like trying to say that two apples plus one orange equals three…what? It doesn’t quite work, does it?

Adding Expressions: A Step-by-Step

So, how do you add entire algebraic expressions? Here’s the lowdown:

Subtracting Expressions: A Little Twist

Subtraction is super similar to addition, but there’s one extra thing to keep in mind:

Let’s See It in Action

• Yes! 7x + 2x = 9x (Like terms, happy family)
• Nope! 4y – y2 = 3y (Those exponents are throwing a wrench in things – not like terms!)
• Heck yeah! 8a + 5b – 2a + b = 6a + 6b (Combining like terms like a boss)
• Watch the signs! (4×2 + 3x) – (x2 – x) = 4×2 + 3x – x2 + x = 3×2 + 4x (Distributing that negative sign makes all the difference)

The Takeaway?

Getting comfortable with adding and subtracting like terms is a huge deal in algebra. Once you get the hang of it, you’ll be able to untangle even the trickiest expressions and solve equations like a pro. So, practice, stick with it, and you’ll be amazed at what you can do!