ADDING & SUBTRACTING MONOMIALS
Learn what monomials and like terms are, study the examples carefully, then take the 5-item seatwork!
What is a Monomial?
A math expression with only one term. It can be a number, a variable, or a number multiplied by variable(s).
Examples: 5x, -3y², 8
What are Like Terms?
Monomials that have the exact same variables raised to the exact same powers. Only the coefficients (numbers) can be different!
Examples: 4x and 9x
Golden Rule: You can ONLY add or subtract LIKE TERMS. If they are not like terms, just leave them as they are! Also, never touch the exponents when adding/subtracting!
Simplify: 4x + 5x
Step 1: Check if like terms. Yes, both have 'x'. →
Step 2: Add the coefficients (4 + 5 = 9). →
Step 3: Keep the variable part exactly the same. →
Final Answer: 9x
Simplify: 12y² - 7y²
Step 1: Check if like terms. Yes, both have 'y²'. →
Step 2: Subtract the coefficients (12 - 7 = 5). →
Step 3: Keep the variable and exponent exactly the same! →
Final Answer: 5y² (Notice the exponent didn't change!)
Simplify: 8a + 3b
Step 1: Check if like terms. 'a' and 'b' are different variables. →
Step 2: Since they are NOT like terms, we cannot combine them. →
Final Answer: 8a + 3b (Just leave it!)
Simplify: -9m + 15m - 2m
Step 1: All terms have 'm', so they are like terms. →
Step 2: Combine the coefficients: -9 + 15 - 2. →
Step 3: -9 + 15 = 6. Then 6 - 2 = 4. →
Final Answer: 4m
Simplify: 6x + 2y - 3x + y
Step 1: Group the like terms together. →
(6x - 3x) + (2y + y) (Note: 'y' means '1y')
Step 2: Combine the 'x' terms: 6 - 3 = 3x. →
Step 3: Combine the 'y' terms: 2 + 1 = 3y. →
Final Answer: 3x + 3y
Simplify: 5a²b - 2a²b + 4ab²
Step 1: Group like terms. 'a²b' and 'ab²' are DIFFERENT! →
Step 2: Combine the 'a²b' terms: (5 - 2)a²b = 3a²b. →
Step 3: '4ab²' has no like term, so it stays. →
Final Answer: 3a²b + 4ab²
Seatwork Time!
Read each question carefully. You need to answer all questions before submitting. Good luck!
Mathemalupit | Interactive Math Review & Seatwork