Do you add or subtract like terms?

Like Terms: Adding, Subtracting, and Why It All Matters (Explained Simply!)

Algebra can seem like a whole different language sometimes, right? And one of the first things you learn is how to simplify expressions. A big part of that? Combining what are called “like terms.” But what are like terms, and how do you actually do it? Turns out, it all boils down to good old addition and subtraction.

So, What Exactly Are “Like Terms”?

Think of it this way: like terms are basically algebraic buddies. They’re terms that have the same variable – that’s the letter, like x or y – raised to the same power. The numbers in front of them? Those can be different. It’s like saying you can add apples to apples, but you can’t really add apples to oranges, can you?

Let’s look at some examples to make it crystal clear:

• 3x and 7x? Total buddies! They both have just a plain old x.
• 5y² and -2y²? Yep, they’re friends too. They both have y squared.
• 4ab and -ab? Absolutely. a and b hanging out together.
• 8 and -11? These are like the quiet friends – just plain numbers, but they’re still like terms.

Now, what about terms that aren’t friends?

• 3x and 3y? Nope. Different letters, different terms.
• 5x² and 5x? Close, but no cigar. The powers are different.
• 4ab and 4a? Not quite. Missing a b in that second one.
• 7 and 7x? One’s a number, one’s a number with a letter. They’re not alike.

Combining Like Terms: It’s All About Adding and Subtracting

Okay, so you know what like terms are. Now, how do you actually combine them? Simple: you add or subtract the numbers in front of them (those are called coefficients), and you leave the variable part exactly as it is. It’s like counting how many apples you have in total.

Here’s the breakdown:

Let’s see it in action:

• 3x + 5x = (3 + 5)x = 8x (Three x’s plus five x’s equals eight x’s.)
• 7y² – 2y² = (7 – 2)y² = 5y² (Seven y squared minus two y squared equals five y squared.)
• 4ab + ab = (4 + 1)ab = 5ab (Remember, if there’s no number in front, it’s like there’s a secret “1” there!)
• 9 – 2 = 7 (Even plain numbers can be combined!)

Why Bother Combining Like Terms?

Why do we even do this? Well, it’s all about making things simpler. A simplified expression is easier to understand, easier to work with, and it’s essential for solving equations and all sorts of other algebra problems. Trust me, you’ll be glad you know how to do this!

Watch Out for These Common Mistakes!

• Mixing Up Unlike Terms: This is the big one. Don’t try to combine things that aren’t alike! 2x and 3x² are not the same.
• Ignoring the Sign: The sign in front of a term is part of that term. So, in 5x – 3y + 2x, that -3y is negative!
• Messing With Exponents: When you combine like terms, the exponent stays the same. 3x² + 4x² is 7x², not 7x⁴.
• Forgetting the Invisible “1”: If you just see x, remember it’s really 1x.

Let’s Do Some Examples Together

Example 1:

Simplify: 3x + 2y – 5x + 4y – z

Example 2:

Simplify: 2a² + 3ab – b² – 5a² + 2b² – ab

Final Thoughts

Combining like terms is a skill you’ll use constantly in algebra. Master it now, and you’ll save yourself a ton of headaches later on. Just remember to add or subtract the coefficients of the like terms, and you’re golden! And hey, if you get stuck, don’t be afraid to ask for help. We’ve all been there!