Adding & Subtracting Polynomials

In this lesson, we will learn how to add and subtract polynomials. Like terms are two or more terms that have the same variable parts (same variable(s) raised to the same power(s)). We can add two or more like terms using the distributive property. Since the variable part is the same in each case, we can pull this outside of a set of parentheses and perform our operation with the coefficients only. Basically, to add two or more like terms together, we add the coefficients (numbers multiplying the variable part) and leave the variable part unchanged. For example: 3x + 9x = x(3 + 9) = 12x. Again, we can just find the sum of the coefficients (3 and 9) and leave the variable part (x) unchanged. To add two or more polynomials together, we just find and add together all the like terms from the polynomials being added. When we subtract polynomials, we have to perform one additional step. Basically, we change the sign of each term of the polynomial that is being subtracted away. Once this is done, we can simply add the two polynomials together. Recall that when we subtract real numbers, we can change the operation into addition of the opposite. We know that: a - b = a + (-b). In this case, the strategy is the same. We can think of this as changing the subtraction to addition and the polynomial that is being subtracted away into its opposite, then performing the addition operation.