In Exercises 29–40, add the polynomials. Assume that all variable...

Question

In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers.

(5x²y + 9xy + 12) + (−3x²y + 6xy + 3)

Accepted Answer

Hello, everyone. We are gonna perform addition in the given expression, the expression we're given is open parentheses. 25 X squared, Y plus seven X Y plus 23 closed parentheses plus open parentheses, negative 15, X squared, Y plus 12, X Y plus three, closed parentheses. Our answer choices are a 10, X squared, Y minus five, X Y plus 26 B 10, X squared, Y plus 19 X Y minus C 10 X squared, Y plus 19 X Y plus D 10 X squared Y plus 19 X Y minus 20. First thing I recall is that if I have a plus sign between two sets of parentheses, I can drop the parentheses and combine my like terms. Since that is the case here when I rewrite this, I'm going to rewrite it without the parentheses. So 25 X squared, Y plus seven X Y plus 23 and then plus a negative 15. So I'm gonna just grade as minus 15, X squared Y plus 12 X Y plus three. Now that I've gotten rid of the parentheses, I'm going to combine my like terms. Recall that like terms have the same variables with the same exponents. And when we rewrite our answer, we want to start with the highest exponents and work our way down. The highest exponents in this expression is X squared Y. So I'm gonna start out by combining 25 X squared Y and negative 15 X squared Y. Again, recall that when you combine like terms, we only combine the coefficients, the variables and exponents stay the same 25 -15 is 10 X squared Y. And I'm gonna cross those out now that I've used them. So I don't try to use them again. Next, I'm gonna use my X Y terms. So I have a seven X Y and A 12 X Y adding those together would give me 19 xy again, we don't change the exponents or the variables, we just add the coefficients. And finally, my constants a positive 23 plus a positive three will give me a positive 26. So my final expression when I add these together is 10 X squared Y plus 19 X Y plus 26. And that's answer choice. C have a nice day.

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In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers. (5x²y + 9xy + 12) + (−3x²y + 6xy + 3)