How Do You Simplify Algebraic Expressions?


Quick Answer

Simplifying algebraic expressions involves removing common factors, simplifying polynomials, and canceling out the same expressions. A properly simplified expression is easier to read and solve, so it's best to factor as soon as possible when solving.

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Full Answer

  1. Remove any common factors to bring the expression to lowest terms

    For example, start with the equation 4x ^2 + 100 = (x + 3)/(x - 5); 4 is a common factor in both 4 and 100, so remove it by using the distributive property. The result ends up as 4(x^2 + 25). Note that not all expressions will have factors to remove.

  2. Simplify polynomials

    Polynomials are expressions with one or more degrees of variable. In the example expression, (x^2 + 25) can be further simplified into (x - 5)(x + 5). When you multiply it by the FOIL method, the middle terms cancel out. This expression is now in simplest form, so now you can move on to the other side of the equation.

  3. Cancel out like terms

    The expression is now in the form 4(x + 5)(x - 5) = (x + 3)/(x - 5). The x + 5 terms, when divided, equal 1, so they can be removed for simplicity. Binomials, such as x + 5, have to be canceled as a whole. The final factored equation is 4(x - 5) = x + 3.

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