Concept Check When directed to completely factor the polynomial 4...

Question

Concept Check When directed to completely factor the polynomial 4x^2y^5-8xy^3,a student wrote 2xy^3(2xy^2-4). When the teacher did not give him full credit, he complained because when his answer is multiplied out, the result is the original polynomial. Give the correct answer.

Accepted Answer

Hello everyone in this video. We're going to be looking at this practice problem where we want to write the complete factory ization of 10 X to the third times Y to the sixth minus 16. X to the fifth, Y to the 10th. So in this case, in order to complete this subtraction, we wanna go ahead and factor out the greatest common factor. So to find the greatest common factor where you have multiple components, where you have numbers such as 10 and 16 and then the X. Variable X to the third, X to the fifth and Y to the sixth and Y to the 10th. It might be easier to look at those similar components. So when we look at 10 and six, the greatest common factor between those two is two. And when I look at X to the third and X to the fifth, the greatest common factor is X to the third. And finally, if I look at Y to the 6th and Y to the 10th. The greatest common factor is why to the 6th. So then this two X to the third, Y to the sixth becomes my greatest common factor. So what I want to do is factor out the greatest common factor from both of these components. 10 X to the third, Y to the 6th and 60 next to the fifth, Y to the 10th. And if I do that, when I factor out two from 10, it becomes five. If I factor out X to the third from X to the third, I'm left with one. And if I factor out Y to the sixth from Y to the sixth I'm left with one as well. So that this first part 10 X to the third, Y to the sixth becomes five times one times one. And if I look at the second part, if I factor two from 16, I'm left with eight. If I factor X to the third from X to the fifth, I'm left with X squared and if I factor Y to the six from Y to the 10th, I'm left with Y to the fourth. So if I simplify this five times one times one, I have five -8 x squared Y to the fourth and I still have the greatest common factor out in front. So two X to the third, Y to the sixth. So because I can't simplify the parentheses any further because I can't subtract eight X squared Y. To the fourth from five, this becomes my final answer. So two X to the third, Y to the six times parentheses, five minus eight X. Squared Y. To the fourth and parentheses. And you can see that that aligns with answer choice D. So hopefully this video helped and see you next time

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Concept Check When directed to completely factor the polynomial 4x^2y^5-8xy^3,a student wrote 2xy^3(2xy^2-4). When the teacher did not give him full credit, he complained because when his answer is multiplied out, the result is the original polynomial. Give the correct answer.