Answer:Just as you can perform the four operations on polynomials with one variable, you can add, subtract, multiply, and divide polynomials with more than one variable. The process is exactly the same, but you have more variables to keep track of. When you are adding and subtracting polynomials with more than one variable, you have to pay particular care to combining like terms only. When you multiply and divide, you also need to pay particular attention to the multiple variables and terms. You can multiply and divide terms that aren’t like, but to add and subtract terms they must be like terms. To add polynomials, you first need to identify the like terms in the polynomials and then combine them according to the correct integer operations. Since like terms must have the same exact variables raised to the same exact power, identifying them in polynomials with more than one variable takes a careful eye. Sometimes parentheses are used to distinguish between the addition of two polynomials and the addition of a collection of monomials. With addition, you can simply remove the parentheses and perform the addition. Some people find that writing the polynomial addition in a vertical form makes it easy to combine like terms. The process of adding the polynomials is the same, but the arrangement of the terms is different. When there isn't a matching like term for every term in each polynomial, there will be empty places in the vertical arrangement of the polynomials. This layout makes it easy to check that you are combining like terms only. You can apply the same process used to subtract polynomials with one variable to subtract polynomials with more than one variable. In order to remove the parentheses following a subtraction sign, you must multiply each term by −1. An alternative to the approach shown above is the vertical method for arranging the subtraction problem. This method is shown below for a different problem. Both methods are effective for subtracting polynomials—the idea is to identify and organize like terms in order to compute with them accurately. The examples that follow illustrate the left-to-right and vertical methods for the same polynomial subtraction problem. Think about which method you find easier. Polynomials with more than one variable can also be multiplied by one another. You use the same techniques you used when you multiplied polynomials with only one variable.
