How Do You Simplify Expressions?


Quick Answer

Expressions are simplified by using the acronym PEMDAS, which stands for parentheses, exponents, multiplication, division, addition and subtraction. This acronym is helpful because it tells the order to perform the mathematical operations in the expression.

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Full Answer

If the expression contains only numbers and operators (no variables), then any operations in parentheses or brackets are performed first. Any exponents present are evaluated. Multiplication and division are equivalent and are evaluated in order from left to right. The same is true for addition and subtraction. The same sequence is followed outside parentheses.

If the expression contains variables in addition to numbers and operators, then like terms must be combined. Like terms need to have the same variables and exponents but do not need to have the same coefficients. For example, 4x and 9x are like terms. When combined, they equal 13x. The terms 2xy^2 and 10xy^2 are also like terms. When combined, they equal 12xy^2. However, 2x and 4y are not like terms because the variables are different, and they can’t be combined. 2x^2y and 10xy are also not like terms because the exponents accompanying the variables are different. After like terms have been combined, the standard order of operations is followed as defined by PEMDAS.

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