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Answer:The are certain things that need to be carefully observed when you add or combine the polynomials. Here is the list of certain rules for adding/combining polynomials.Step-by-step explanation:The are certain things that need to be carefully observed when you add or combine the polynomials - especially the polynomials with more than one variable. Here are some of the rules for adding polynomials: First we must identify like terms in the given polynomials, and then combine them based on the correct integer operations.When there is a plus sign, we add polynomials. It must be noted that, within polynomials, we need to add or subtract like terms. For example, when we combine like terms, such as 4x and 5x, we tend to add their coefficients i.e. 4x + 5x = 9xPlease remember we can not add polynomials if they have different exponents. For example, x²+ x can not be added. Lets add and simplify the following polynomials. (4x + 7y) + (5x – 3y) First clear the parenthesis. 4x + 7y + 5x – 3yThen make sue to group the like terms in accordance to their variables - try to keep them in alphabetically order, and ultimately just simplify.4x + 5x + 7y - 3y9x + 4ySo, 9x + 4y is the answer.Note: I can not further combine or add 9x + 4y as they are un-like. The reason is simple; un-like polynomials have different variables. The polynomials can be add vertically too.Just put each variable in its own columnFirst column can be termed as x-column and second column can be termed as y-columnChoosing the horizontal or vertical method is just a matter of taste.Here is the vertical method of adding (4x + 7y) and (5x – 3y) .4x    +7y5x     -3y________9x + 4y________Keywords: add, combine, polynomials Learn more about adding polynomials from  brainly.com/question/817 #learnwithBrainly