3x² and 5x are NOT like terms — x² and x have different exponents, so they represent different 'units' (copies of x-squared vs. copies of x). They cannot be combined, just as you cannot add 3 square feet and 5 feet into a single measurement. The most common wrong answer is 8x², which incorrectly adds the coefficients as if the terms were alike.
Question 2 Multiple Choice
Simplify: 4x + 2y + 3x − y
A9xy
B9x
C7x + y
D7x + 3y
Group like terms separately: (4x + 3x) = 7x, and (2y − y) = 2y − 1y = 1y = y. Result: 7x + y. Key trap: 'y' alone means 1y (an invisible coefficient of 1), so 2y − y = 1y = y, not 2y. Option A wrongly multiplies variables together. Option D incorrectly handles the subtraction, treating −y as though it were +y.
Question 3 True / False
The expression 6a − a simplifies to 5a, because 'a' has an implied coefficient of 1.
TTrue
FFalse
Answer: True
Correct. Any variable written without a visible coefficient has a coefficient of 1: a = 1a. So 6a − a = 6a − 1a = (6 − 1)a = 5a. This applies universally — x means 1x, y² means 1y², and so on. Forgetting the invisible 1 is one of the most common errors in simplifying expressions.
Question 4 True / False
When combining like terms such as 3x³ + 5x³, you add the exponents to get 8x⁶.
TTrue
FFalse
Answer: False
Exponents are never added when combining like terms. 3x³ + 5x³ = (3 + 5)x³ = 8x³ — the exponent stays the same because you are adding the counts of copies of x³, not multiplying. Exponents add only when you multiply terms (e.g., x³ · x³ = x⁶). Combining like terms is coefficient addition, which leaves the variable and its exponent unchanged.
Question 5 Short Answer
Explain why 3x and 5x can be combined into 8x, but 3x and 5x² cannot be combined. Use the idea of 'counting copies.'
Think about your answer, then reveal below.
Model answer: 3x means '3 copies of x' and 5x means '5 copies of x' — they count the same unit, so you add the counts: 3 + 5 = 8 copies of x, giving 8x. But 3x means '3 copies of x' and 5x² means '5 copies of x-squared,' which are different units entirely (like feet vs. square feet). You cannot add counts of different things into a single number, so the expression stays as 3x + 5x².
The underlying mechanism is the distributive property: 3x + 5x = (3 + 5)x = 8x. The variable is the common factor being 'counted'; the coefficients are the counts. Different exponents mean different variables in the sense that x and x² are different quantities — just as distance and area are different even though they both measure physical things.