Like and unlike terms

The idea

Terms with the same letter-numbers are like terms; terms with different letter-numbers are unlike terms.

Pencils and erasers

A shop sells pencils at c rupees each and erasers at d rupees each. On Day 1 it sold 5 pencils and 4 erasers.

Money from pencils: 5c. Money from erasers: 4d.

On Day 2 it sold 3 pencils (3c) and 6 erasers (6d). Which two amounts are the same kind of money, so they could be added into one term?

• 5c and 3c: both are pencil money
• 5c and 6d
• 4d and 3c

Find the like terms

A target term is shown. Tap every term that is the same kind: it has the same letter-number.

Same letter-numbers

Terms are like when they have the same letter-number. The number parts and the signs can differ. Terms with different letter-numbers are unlike.

Terms with the same letter-numbers are like terms; terms with different letter-numbers are unlike terms.

• Terms | Kind
• 5c, c, 10c | like terms: all have c
• 12n, −4n | like terms: both have n
• 18c, 11d | unlike terms: c and d

Notes

Terms with the same letter-numbers are like terms; terms with different letter-numbers are unlike terms.

Check yourself

Which pair are like terms?

Are 8n and −3n like terms?

In 3a + 5b + 2a + b, which term is like 5b?

How many of the terms 4x, 9y, x, 6x, 2y are like 4x? Count 4x itself.

Answer: 3

4x, x and 6x have the letter-number x.

• 7x and 7y. The number 7 is the same, but x and y are different letter-numbers.
• 7x and 7. 7 has no letter-number, so it is not like 7x.
• 7x and 12x — correct. Yes! Both have the letter-number x.
• No: one of them is negative.. The sign does not matter. Both have the letter-number n.
• No: the numbers 8 and 3 are different.. The number parts may differ. What matters is the letter-number.
• Yes: both have n. Only the number parts differ. — correct. Yes! The sign and the number do not matter.
• 2a. 2a has the letter-number a.
• b — correct. Yes! b is 1 × b, so it has the same letter-number b.
• 3a. 3a has the letter-number a.