Question

From the following pairs, find the pairs of like terms.

(1) 7y, 2y
(2) 5ab, 9ba
(3) pq², 2p²q
(4) 5pq, 5py
(5) 4x²yz, 8xy²z
(6) 11ax², 10x²a
(7) 3pqr, 4p²qr

Answer 1

Like Terms: These are the terms that contain the same variables raised to the same power.
Unlike Terms: These are the terms that contain the same or different variables raised to different powers.

(1)7y, 2y
In 7y and 2y, variable is y and the index of y in each term is 1.
∴ 7y, 2y are like terms.

(2) 5ab, 9ba
In 5ab and 9ba, variables are a and b and in each term index of a is 1 and index of b is 1.
∴ 5ab, 9ba are like terms.

(3) pq², 2p²q
In pq² and 2p²q, variables are p and q and in the first term, index of p is 1 and index of q is 2, whereas in the second term, index of p is 2 and index of q is 1.
∴ pq² and 2p²q are unlike terms.

(4) 5pq, 5py
In the first term, 5pq, variables are p and q, whereas in the second term, 5py, variables are p and y.
∴ 5pq and 5py are unlike terms.

(5) 4x²yz, 8xy²z
In 4x²yz and 8xy²z, variables are x, y, and z and in the first term, index of x is 2 and index of y is 1 and index of z is 1. In the second term, index of x is 1, index of y is 2 and index of z is 1.
∴ 4x²yz and 8xy²z are unlike terms.

(6) 11ax², 10x²a
In 11ax² and 10x²a, variables are a and x and in each term, index of a is 1 and index of x is 2.
∴ 11ax² and 10x²a are like terms.

(7) 3pqr, 4p²qr
In 3pqr and 4p²qr, variables are p, q and r and in the first term, index of p is 1, index of q is 1 and index of r is 1. In the second term, index of p is 2, index of q is 1 and index of r is 1.
∴ 3pqr and 4p²qr are unlike terms.