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When Adding or Subtracting Expressions How Do You Identify the Like Terms?

A mathematical expression contains variable(s) and number(s) combined using the algebraic operations of addition, subtraction, multiplication and division. Unlike an equation, an expression doesn't have an equal sign and thus can't be solved for the variable. Expressions are instead simplified or evaluated, using a given solution for the variable that can plug back into the expression. Expressions can include exponents on the variables. Exponents denote how many times the variable should be multiplied by itself. For example, x^2 equals x * x.

Instructions

Adding Expressions
- 1
  Add two expressions by simply adding together like terms. Group together terms that are alike, meaning they are either numbers without any variable or are terms with exactly matching variables: for example, 3 and 5 are like terms and 3x and 5x are like terms but 3y and 5x aren't like terms because the x and y represent different values.
- 2
  Add the expressions 3x^2y + 4xy + 3x + 2y + 8 and 6x^2y + 2xy + 3y + 2. Group together the like terms, maintaining the algebraic operation: 3x^2y + 6x^2y + 4xy + 2xy + 3x + 2y + 3y + 8 + 2. Note that the 3x is the sole term with only an "x" variable and thus can't be combined with anything else.
- 3
  Add the like terms: 3x^2y + 6x^2y = 9x^2y; 4xy + 2xy = 6xy; 3x = 3x; 2y + 3y = 5y and 8 + 2 = 10. Write the answers back in the expression, maintaining the algebraic operation: 9x^2y + 6xy + 3x + 5y + 10.
Subtraction
- 4
  Subtract two expressions by placing each inside a set of parenthesis. Distribute the minus sign as a negative sign through the second set of parenthesis, changing operations where necessary. Gather the like terms and simplify the expression.
- 5
  Subtract the expression 3x^2 + 4y - 9 from the expression 6x^2 + 8y + 3. Write out the operation: (6x^2 + 8y + 3) - (3x^2 + 4y - 9). Distribute the minus sign through the second set of terms: 6x^2 + 8y + 3 + -3x^2 + -4y + 9.
- 6
  Group together the like terms, maintaining the algebraic operations: 6x^2 + -3x^2 + 8y + -4y + 3 + 9. Add like terms: 6x^2 + -3x^2 = 3x^2; 8y + -4y = 4y; and 3 + 9 = 12. Place the answers back in the simplified expression: 3x^2 + 4y + 12.

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