In Exercises 41–50, subtract the polynomials. Assume that all var...

Question

In Exercises 41–50, subtract the polynomials. Assume that all variable exponents represent whole numbers.(7y²ⁿ + yⁿ − 4) − (6y²ⁿ − yⁿ − 1)

Accepted Answer

Hey, everyone in this problem, we're asked to perform subtraction in the given expression. And we're told to let and represent a whole number. The expression mark given is four Y to the exponent two N plus nine, Y to the exponent N minus seven minus the entire expression six Y to the exponent two, N minus two Y to the exponent N minus eight. We're given four answer choices. Option A two Y to the exponent two N plus 11 Y to the exponent N plus one. Option B 10, Y to the exponent two N plus seven, Y to the exponent N plus one. Option C negative two Y to the exponent two N plus seven, Y to the exponent N minus 15. And option D negative two, Y to the exponent two N plus 11 Y to the exponent N plus one. We're gonna start by rewriting the expression we were given in brackets. We have four Y to the exponent to N plus nine Y to the exponent N minus seven. Then we're gonna subtract the other expression in brackets six Y to the exponent to N -2, Y to the exponent N minus eight Now, in order to simplify this, we wanna first expand. OK. So we wanna get rid of the brackets. Now, in order to get rid of the second bracket, we're subtracting the entire expression. So that subtraction or that negative needs to apply and be distributed to every term in that second expression. If we do that, we get four Y to the exponent two N plus nine Y to the exponent N minus seven -6 Y to the exponent two N plus two Y to the exponent N plus eight. So the terms of the second bracket, six Y to the exponent two N that were positive end up being subtracted because we're subtracting a positive value that gives us a subtraction. The terms that were subtracted to Y to the exponent N and A are now being added because we're subtracting a negative value a negative multiplied by a negative gives a positive. So subtracting a negative is the same as adding. Now we've expanded this expression as much as we can and to simplify it, we want to collect like terms. Starting on the left hand side, we have four Y to the exponent two N. We want to look and see if there are any other like terms. Are there any other terms that have Y to the exponent two N? Yeah, we have M -6 Y to the exponent two N later in our equation. So four Y to the exponent two N minus six Y to the exponent to N gives us negative two Y to the exponent two N. In the first term in our resulting expression, we move to the next term we have 9 y to the exponent N and we also have plus two Y to the exponent end nine Y to the exponent N plus two Y to the exponent N gives us 11 Y to the exponent N. So we add 11 Y to the exponent N to our resulting expression. We move to the next term in our expanded expression, we have -7. Later on. In our equation, we add eight. So negative seven plus eight gives us plus one in our resulting expression. Now we've performed the subtraction, we've simplified the result as much as we can. Yeah. And so the resulting expression is negative two Y to the exponent two N plus 11 Y to the exponent N plus one which corresponds with answer choice. D. Thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 41–50, subtract the polynomials. Assume that all variable exponents represent whole numbers.(7y²ⁿ + yⁿ − 4) − (6y²ⁿ − yⁿ − 1)

Key Concepts

Polynomials

Subtracting Polynomials

Combining Like Terms

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