Adding single variable terms with exponents is a common operation in evaluating algebraic expressions. For example, 3x^2 + 5x^2 = (3+5) x^2 = 8x^2. The numbers 3 and 5 are called coefficients and should be added while the variable and exponents are kept the same. If the coefficient is not displayed in front of the variable, then assume it to be 1. For example: x^5 + x^5 = (1+1) x ^5 = 2x^5.
Adding multiple like variable terms where the exponents are also the same involves adding the coefficients and exponents while keeping the variables the same. An example: (1x^2 + 1y^2) + (1x^2 + 1y^2) would result in (1+1) x^2 + (1+1) y^2 = 2x^2 + 2y^2.
Adding multiple variable terms where exponents are unlike cannot be done. For example, 1x^2 + 1x^3 cannot be added because exponents are not the same. In this case, the expression is left in its simplest form.
Adding multiple variable terms with exponents where the exponents are both unlike cannot be done because the variables are not the same. For example, 1x^2 + 1y^2 cannot be added so must be left in its already simplest form. In addition, cases where the variables and exponents are unlike also cannot be added. So, the example, 2x^2 + 2y^3 cannot be added because the variables and exponents are not the same.