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How to Combine Like Terms With Different Symbols

A term, the basic unit of an algebraic expression, is composed of two parts: a number and one or more variables. It may also have an exponent, though an exponent is not a necessary component of a term. Like terms are terms that have the same variables and exponents. They may have different numerical coefficients. For example, 1a^b and 45a^b are like terms; 1a^b and 45ab^2 are not like terms. Only like terms can be combined. Remember that a minus sign to the left of a term belongs to that term. In the expression 2x-3y+5y the terms are 2x, -3y and 5y. The minus sign tells us that 3y is a negative term.

Instructions

    • 1

      Add like terms with the same sign by adding the numerical coefficients and keeping that sign:

      ab^2 + 2ab^2 = 3ab^2

      -2xy-3xy = -5xy

      -4a+(-6a) = -10a

    • 2

      Add like terms with opposite signs by subtracting the smaller term from the larger term. Keep the sign of the larger term:

      -5a+a = -4a

      7y+(-3y) = 4y

    • 3

      Subtract a negative term by following the formal rule -(-a) = a:

      2x-(-3x) = 2x + 3x = 5x

      3-(-6) = 3+6 = 9

      -6y -(-3y) = -6y +3y = -3y

    • 4

      Combine a long series of terms by grouping like terms together for ease of calculation:

      6a -7b-3a+4b = 6a-3a-7b+4b = 3a-3b

    • 5

      Remember that a negative term times a negative term yields a positive term. A negative term times a positive term yields a negative term.

    • 6

      Multiply (and divide) like terms with an odd number of negative signs by multiplying the numerical coefficient and and putting in a negative sign. So, the result is negative:

      -7y*-3y*-2y = -42y.

      With an even number of negative signs the result is positive:

      -7y*-3y = 21y

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