Collecting Like Terms

We say that a, 2a, 3a, -7a, 100a are like terms because they are of the same kind. But 5a is not of the same as 5b

2a and 3b are unlike terms. When we are simplifying expressions, we collect the like terms together then do the addition and subtraction.

The expression a + ab remains as it is because a and ab are unlike terms. We cannot simplify any further.

Similarly, the expression a + { a }^{ 2 } + { a }^{ 3 } remains as it is because a, { a }^{ 2 }, { a }^{ 3 } are all unlike terms. We cannot add or subtract unlike terms from the terms. Always remember this.

Let’s look at some examples.

Example

Simplify:

i) 2a + 3ab - a - ab

ii) 2a + { a }^{ 2 } + 3a + { 5a }^{ 2 }

iii) 3ab - abc + 5ab - 2abc

iv) { x }^{ 2 } + { 5y }^{ 2 } + { 3x }^{ 2 } - { y }^{ 2 }

v) a + { a }^{ 2 } + { a }^{ 3 } + b + { b }^{ 2 } + { b }^{ 3 } - { 2a }^{ 2 } - { 3b }^{ 3 }

i) 2a + 3ab - a - ab

= 2a + 3ab -ab

= a + 2ab

ii) 2a + { a }^{ 2 } + 3a + { 5a }^{ 2 }

= 2a + 3a + a^{2} + 5a^{2}

= 5a + { 6a }^{ 2 }

iii) 3ab - abc + 5ab - 2abc

= 3ab + 5ab - abc - 2abc

= 8ab + (-3abc)

=8ab - 3abc

iv) { x }^{ 2 } + { 5y }^{ 2 } + { 3x }^{ 2 } - { y }^{ 2 }

= { 4x }^{ 2 } + { 4y }^{ 2 }

v) a + { a }^{ 2 } + { a }^{ 3 } + b + { b }^{ 2 } + { b }^{ 3 } - { 2a }^{ 2 } - { 3b }^{ 3 }

= a - { a }^{ 2 } + { a }^{ 3 } + b + { b }^{ 2 } - { 2b }^{ 3 }