← Chapter 46 Chapter 47: Collecting Like Terms (Advanced) Chapter 48 →

Chapter 47: Collecting Like Terms (Advanced)

✏️ Explanation

Collecting like terms means combining terms with the same variables and powers. This includes more complex expressions with multiple variables.

🔍 Why It Matters

Simplifying expressions is essential for solving equations and working with formulas.

✏️ Worked Example

Simplify: 3x² + 5x - 2x² + 7 - 3x + 1
Step 1: Group like terms together
(3x² - 2x²) + (5x - 3x) + (7 + 1)
Step 2: Combine each group
x² + 2x + 8

🔢 Practice Exercises

1. Simplify: 4a + 3b - 2a + b
Answer:
2. Simplify: 2x² + 3x - x² + 5x - 4
Answer:
3. Simplify: 5y - 3 + 2y² - y + 7
Answer:
4. Simplify: 3ab + 2a - ab + 4b
Answer:
5. Simplify: x² + 2xy + 3x² - xy + y²
Answer:

⚠️ Common Mistakes

  • Combining unlike terms (x and x²)
  • Dropping negative signs
  • Forgetting constant terms

✨ Quick Summary

Only combine terms with identical variables and powers. Keep track of signs.