Collecting like terms

Remember that any term containing the same letter can be combined by adding and subtracting.

So: 3g + 3k + 5g + 4k - g

= 3g + 5g - g + 3k + 4k

= 7g + 7k

curriculum-key-fact
Like terms that include powers can only be added or subtracted if the powers are the same. Like terms with different powers cannot be added or subtracted.

Example

Simplify:

3x + 5 + {x}^{2} - 2x + {2x}^{2} - 1

Solution

Rearrange the expression so that like terms with the same powers are next to each other:

{x}^{2} + {2x}^{2} + 3x - 2x + 5 - 1

And then simplify:

{3x}^{2} + x + 4

We usually write the expression with the {x}^{2} term first, then the {x} term, and finally the number term.

Question

Simplify:

5 + 4x^2 - 3 + 2x + x^2 - 4x

To get the answer, rearrange the expression:

4x^2 + x^2 + 2x - 4x + 5 - 3

and then simplify:

5x^2 - 2x + 2