Simplify Like Terms With Several Variables

When we simplify algebraic expressions, we combine like terms. 

Like terms are terms with matching letters.

3a, 4a and a are like terms because they are all multiples of a.

2b, -b, -5b are like terms because they are all multiples of a - even though some of them are negative.

2b and b² are not like terms: 2b means 2 x b and b²  means b x b.

3b and 3 are not like terms: 3b is a multiple of b and 3 is not.

3b, 5c and -2 are not like terms: there is a multiple of b, a multiple of c and a number.

Example

Simplify -4 + 3b + 4b - a + 2b + 6a + 3

Answer

Look at the values before all the as (known as the coefficients):  -a + 6a which are -1a + 6a

Combine them to get  -1 + 6 = 5

So we get 5a

Look at the coefficients of all the bs...... 3b + 4b + 2b which are 3b + 4b + 2b

Combine them to get 3 + 4  + 2 = 9

So we get 9b

Combine the numbers which are -4 + 3 = -1

The answer is 5a + 9b - 1

Let's have a go at some questions.