Subtract −5a²b⁴ − 8ab² − ab from 3a²b⁴ − 5ab² + 7ab.

Question

Accepted Answer

Hey, everyone in this problem, we're asked to perform subtraction as indicated negative seven P cubed Q to the exponent five minus five P Q cubed minus P Q from eight P cubed Q to the exponent five minus six P Q cubed plus two P Q. All right. That can be a little bit confusing to read math in words. So let's just write out what this question is asking for us. They're asking us to perform subtraction. OK. The first expression given from the 2nd expression. So when we convert this into mathematical notation, OK, we have the first expression subtracted from the second. So we're gonna write the second expression first eight P Q Q to the exponent five minus six P cute, cute Plus 2 PQ. And we want to subtract the other expression from this one. So we're gonna subtract negative 7 p cubed Q to the exponent 5 -5 PQ Cubed -2Q. So this is what the question is asking us to do. In terms of the math, we're given four answer choices, option A 15 P cubed Q to the exponent five plus P Q cubed plus three P Q option B 15 p cubed Q to the exponent by minus P Q cubed minus three P Q option C 15 P cubed Q to the exponent five plus P Q cubed minus three P Q in option D 15 P cubed Q to the exponent five minus P Q cubed plus three P Q. So we've written out what we're trying to solve here. Now, in order to perform this subtraction, the first thing we wanna do is expand this entire expression we have, OK. So we want to get rid of these brackets. Now, in order to get rid of the brackets from the second part of our expression, and we're subtracting the whole expression. That means that the negative needs to apply to every single term in the brackets. Now, every term in that bracket is being subtracted. OK? It's already negative. So we have a negative multiplied by a negative. This is gonna give us a positive for each of these terms. So each of these terms is gonna end up being added in our expression. So if we write this out, we have eight P cubed Q to the exponent five minus six P Q Q plus two P Q plus 7 p cubed Q to the exponent five Plus 5 PQQ um plus P Q. So now we've expanded our expression, we've gotten rid of those brackets. And what we're left to do is to simplify. So we wanna collect like terms. Let's start on the left hand side, we have a P cubed Q to the exponent five term. We wanna look and see if there are any others. And we do have another. So we have eight P cubed Q to the exponent five plus seven P cubed Q to the exponent five, which gives us 15 P cubed Q to the exponent five. We move to our next term. We have -6 PQ cubed. We want to look for any other terms that match this. So we have plus five P Q cubed, negative six P Q cubed plus five P Q cubed gives us minus P Q cubed in our resulting expression moving to the next term we have plus 2 PQ and we also have plus P Q at the end. So two P Q plus P Q gives us three P P Q and we add that on to our expression. Now we've dealt with every single term in our expanded expression. We've simplified collected like terms and we have our resulting expression and we perform the subtraction. We simplify it as much as we can and we get the result is P cubed Q to the exponent five minus P Q cubed plus three P Q which corresponds with answer choice. D. Thanks everyone for watching. I hope this video helped see you in the next one.

Subtract −5a²b⁴ − 8ab² − ab from 3a²b⁴ − 5ab² + 7ab.

Key Concepts

Polynomial Subtraction

Like Terms

Distributive Property

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