Combining Like Terms
Like terms are terms that have the same variable(s) raised to the same power. For example, the terms 3x², -2x², and 5x² are all like terms because they all have the variable x raised to the power of 2. The terms 3x² and 5x are not like terms because they have different powers of the variable x.
To combine like terms, we simply combine the coefficients of the terms. The coefficient of a term is the number that is multiplied by the variable(s). For example, the coefficient of the term 3x² is 3.
To combine like terms, we can use the following steps:
- Identify the like terms in the expression.
- Combine the coefficients of the like terms.
- Make sure to keep the variable(s) and exponents the same.
- Check to make sure that you have combined all of the like terms.
Here are some examples of combining like terms:
- 3x² + 5x - 2x² - x = x² + 4x
- 3x² + 2xy - 5y² + 4xy = 3x² + 6xy - 5y²
You should combine like terms whenever you are simplifying an algebraic expression. Combining like terms can make the expression easier to read and understand, and it can also make it easier to solve equations.
Here are a couple more complicated examples of combining like terms:
- (2x² + 3x - 5) + (-x² + 2x + 4) = x² + 5x - 1
- (4x² - 3x + 2) - (3x² + 2x - 1) = x² - 5x + 3