Grade 7 maths multiple choice questions on like terms in algebra with detailed step-by-step solutions. Click the arrow below each question to reveal the explanation.
Like terms in algebra are terms containing the same variables raised to the same exponent (or power). Like terms may have different numerical coefficients.
$2x$, $-3x$, $\dfrac{1}{2}x$, and $0.1x$ are all like terms since they contain the same (one) variable $x$ to the same power 1. (Note: $x = x^1$)
$2x$ and $-4x^{2}$ are not like terms because they contain the same variable $x$ but raised to different powers. In $2x$, the exponent of $x$ is 1, while in $-4x^{2}$, the exponent of $x$ is 2.
$-\dfrac{1}{2}xy^{2}$ and $8xy^{2}$ are like terms because they contain the same variables $x$ and $y$ raised to the same powers: the exponent of $x$ is 1 in both terms, and the exponent of $y$ is 2 in both terms.
$5x^{3}y^{2}$ and $-11xy^{2}$ are not like terms because they contain the same variables $x$ and $y$ but not raised to the same powers. In $5x^{3}y^{2}$, the exponent of $x$ is 3, while in $-11xy^{2}$, the exponent of $x$ is 1.
Answer: C
For terms to be "like", they must have the exact same variables raised to the exact same powers. In list C, every single term contains the variable $x$ raised to the power of 1. Constants (like 4 or -3) or differing powers (like $x^2$ or $\dfrac{1}{x}$) make the other lists contain unlike terms.
Answer: D
A like term must have exactly the variables $x$ and $y$, both raised to the power of 1. The coefficient (the number in front) does not matter. Only $-10xy$ meets this criteria.
Answer: B
List B contains a mix of different variables and powers ($x^1$, $x^2$, $xy$, and a constant $9$). Therefore, they are unlike terms. Note that list D contains only constants, which are considered like terms to each other.
Answer: D
In list D, every term contains the exact same variable combination $xy$ raised to the same power (1). List C is incorrect because it includes a term with just $x$ ($0.002x$).
Answer: A
The order of multiplication does not matter due to the commutative property ($x^2y = yx^2$). Term A ($-4yx^{2}$) has $x$ raised to the power of 2 and $y$ raised to the power of 1, exactly matching the variables in $-x^{2}y$.
Answer: C
We are looking for the term that does not match $x^1y^2$. Option C has $y$ raised to the power of $-2$ instead of $2$. (Note: Option A is a like term because $y^2x$ is the same as $xy^2$).
Answer: B
List B contains terms with varying variables and powers (e.g., $x^2y^2$ vs $x^2y$). All other lists contain terms that share identical variable components or are all purely constants.
Answer: D
In list D, all terms contain $x$ to the 3rd power and $y$ to the 3rd power. The order in which the variables are written (e.g., $y^3x^3$) does not change the term.
Answer: C
Terms A, B, and D all have $x$ to the 1st power and $y$ to the 4th power. Term C is different because it has $x$ raised to the 4th power.
Answer: D
The term $-9$ is a constant (a number with no variables). Any other constant is a like term. Option D contains the variable $x$, making it unlike. (Note: In Option A, anything raised to the power of 0 equals 1, making $-4.99y^{0}$ effectively just the constant $-4.99$).