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.

(7x²y − 5xy) + (2x²y − xy)

Accepted Answer

Hello, everyone. We're gonna perform addition. In the given expression, the expression we're given is open parentheses. Nine X squared, Y minus five X Y closed parentheses plus open parentheses. Five X squared, Y minus two X Y closed parentheses. Our answer choices are a 14 X squared, Y plus seven X Y B 14 X squared, Y minus seven X Y C 14 X squared, Y minus three X Y D four X squared Y minus seven X Y. First thing I recall is that when I'm dealing with the addition of expressions, I can drop my parentheses and add the like terms as if I was just combining like terms. If this is a minus sign, we could not do that. But since it is a plus sign, I'm gonna rewrite this without my parentheses. So 9 x squared, Y minus five X Y plus five X squared, Y minus two X Y. Now I'm gonna combine my like terms. Recall that like terms are the same variables with the same exponents here. My first set of like terms I'm gonna deal with are the X squared Y terms. So I have nine X squared Y and five X squared Y, we're gonna combine our coefficients, nine plus five is 14 and the variables in exponents do not change. So 14 x squared y next, I'm gonna combine my X Y terms. I have a negative five X Y and a negative two X Y. Those will combine to be a negative seven X Y. And again, the variables in the exponents do not change. These are not like terms and they cannot be combined any further. So our answer is 14 X squared Y minus seven X Y. And that's answer choice B have a nice day.

In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers. (7x²y − 5xy) + (2x²y − xy)

Key Concepts

Polynomials

Like Terms

Combining Polynomials

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