# How to Combine Like Terms

Rules for Combing Like Terms

### Video on how to combine Like Terms

Examples of Like Terms Examples that are NOT like Terms
3 + 2 3 + x
x + 2x x + 2
3x + 5x 3x2 + 5x
x2 + 3x2 x2 + 3x3
2x21 + 3x21 2x23 + 3x21
2xa + 3xa 2xa + 3xab ($$b \ne 1$$)
• Exponents and Bases: You may have noticed that like terms always have the same base and exponent.
• Regarding Coefficients: Also, the coefficient in front of a variable does not change whether or not terms are alike. For instance 3x and 5x and 11x are all like terms. The coefficients ( the '3' in 3x, '5' in 5x and '11' in 11x) do not have anything at all to do with whether or not the terms are like. All that matters is that each of 'x' factors or 'bases' have the same exponent.

### Practice Combining Like Terms

x and 2x are like terms so you combine, or add, them to become 3x. Therefore the final answer is 3x +2
5 and 2 are like terms so you can combine them to become 7. Therefore the final answer is 7 +x
3x and 2x are like terms (Remember the coefficients do not matter) so you can combine (ie 'add') them to become 5x. The final answer is 5x + 6

2x and x are like terms so you can combine (ie 'add') them to become 3x. Likewise, 3 and 6 are like terms and can be added to 9. The final answer is 3x + 9

### More Challenging problems

2x2 and x2 are like terms so you can combine (ie 'add') them to become 3x2. Likewise, 13 and 6 are like terms and can be added to 19. The final answer is 3x2 + 19

2x3 and 4x3 are the only like terms --combine (ie 'add') them to become 6x3. Likewise, 13 and 6 are like terms and can be added to 19. The final answer is 6x3 +x2 + 3x