combine like terms
Adding or subtracting terms that have the same variable(s) and exponent(s).
Combining like terms refers to combining variables or constants that have the same or similar terms. This is done by adding or subtracting the coefficients of these terms.
For example, consider the expression, 3x + 2x. The terms with variables are 3x and 2x. These terms have the same variable (x) and can, therefore, be combined by adding their coefficients (the numbers in front of the variables). The coefficients of 3x and 2x are 3 and 2, respectively. Thus:
3x + 2x = (3 + 2)x = 5x
Therefore, the expression 3x + 2x can be simplified to 5x.
Another example is 4a – 2b + 3a + 5. In this expression, the terms with variables are 4a and 3a. These terms have the same variable (a) and can be combined by adding their coefficients. The coefficients of 4a and 3a are 4 and 3, respectively. Thus:
4a + 3a = (4+3)a = 7a
The term -2b cannot be combined with any other term since it does not have the same variable. Thus:
4a – 2b + 3a + 5 = 7a – 2b + 5
Therefore, the expression 4a – 2b + 3a + 5 can be simplified to 7a – 2b + 5.
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