Real-World Examples of Simplifying Algebraic Expressions

📚 Quick Study Guide

• 🧮 Combining Like Terms: Identify terms with the same variable and exponent, then add or subtract their coefficients. Example: $3x + 2x = 5x$
• ➕ Distributive Property: Multiply a term by each term inside parentheses. Example: $a(b + c) = ab + ac$
• ➖ Order of Operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
• ➗ Factoring: Find common factors and rewrite the expression. Example: $4x + 8 = 4(x + 2)$
• 💡 Simplifying Fractions: Reduce fractions by dividing both the numerator and denominator by their greatest common factor. Example: $\frac{6x}{3} = 2x$
• 📌 Key Tip: Always double-check your work and ensure all possible simplifications have been made.

🧪 Practice Quiz

1. What is the simplified form of $2x + 5y - x + 3y$?
   1. $x + 8y$
   2. $3x + 8y$
   3. $x + 2y$
   4. $3x + 2y$
2. Simplify: $3(a + 2b) - b$
   1. $3a + 5b$
   2. $3a + 7b$
   3. $3a + b$
   4. $3a + 6b$
3. What is the simplified form of $\frac{10x + 5}{5}$?
   1. $2x + 1$
   2. $5x + 1$
   3. $2x + 5$
   4. $10x + 1$
4. Simplify: $4m - 2(m - 3)$
   1. $2m + 6$
   2. $2m - 6$
   3. $6m - 6$
   4. $6m + 6$
5. What is the simplified form of $x^2 + 3x - 4 + 2x^2 - x + 1$?
   1. $3x^2 + 2x - 3$
   2. $3x^2 + 4x - 5$
   3. $x^2 + 2x - 5$
   4. $3x^4 + 2x^2 - 3$
6. Simplify: $5(2p - 3) + 10$
   1. $10p - 5$
   2. $10p - 25$
   3. $7p + 5$
   4. $10p + 5$
7. What is the simplified form of $7y - (3y + 2)$?
   1. $4y - 2$
   2. $10y + 2$
   3. $4y + 2$
   4. $10y - 2$