Combining like terms means adding or subtracting terms that have the exact same variable part.

Like terms have:

✅ the same variable(s)
✅ the same exponent(s)

Example of like terms:

• $3x$ and $-5x$ ✔️

• 7y^2 and 2y^2 ✔️

• 9 and $-4$ ✔️ (constants are like terms)

NOT like terms:

• x and x^2 ❌ (different exponents)

• $2x$ and $2y$ ❌ (different variables)

• $3ab$ and $3a$ ❌ (different variable parts)

🧠 Why can we combine them?

Because they’re the same “type” of thing.

Example:

2x + 5x

That’s like saying:

• 2 apples + 5 apples = 7 apples
  So:

2x + 5x = 7x

⭐ The Key Rule

When combining like terms:

Add/subtract the coefficients

and keep the variable part the same.

Example:

8x – 3x = 5x

Because:

• coefficients: 8 and -3

• 8 + (-3) = 5

🔥 Step-by-Step Example (Beginner Friendly)

Simplify:

4x + 7 + 2x – 3

Step 1: Group like terms

• $4x$ and $2x$ are like terms

• 7 and $-3$ are like terms

Step 2: Combine them

(4x + 2x) + (7 – 3)

6x + 4

✅ Final answer:

6x + 4

⚠️ Common Mistakes to Avoid

❌ Mistake 1: Combining unlike terms

3x+5≠8x

You cannot combine a variable term and a constant.

❌ Mistake 2: Forgetting negative signs

6x – 9x = -3x

Not $3x$

❌ Mistake 3: Combining different powers

2x^2 + 3x^2 = 5x^2

But:

2x^2 + 3x