<h2>Steps:</h2>
So firstly, we need to factor out the GCF. Since all the terms share a GCF of x, factor that out as such:
![(x)(x^2y^2-x^4+y^3-yx^2)](https://tex.z-dn.net/?f=%28x%29%28x%5E2y%5E2-x%5E4%2By%5E3-yx%5E2%29)
Next, I will be factoring by grouping. For this, factor x²y² + y³ and -x⁴ - yx². Make sure that they have the same quantity on the inside:
![(x)(y^2(x^2+y)-x^2(x^2+y))](https://tex.z-dn.net/?f=%28x%29%28y%5E2%28x%5E2%2By%29-x%5E2%28x%5E2%2By%29%29)
Now rewrite the expression as:
![(x)(y^2-x^2)(x^2+y)](https://tex.z-dn.net/?f=%28x%29%28y%5E2-x%5E2%29%28x%5E2%2By%29)
However, we can factor this expression further. Next, we will be applying the difference of squares rule, which is
. In this case:
![y^2-x^2=(y+x)(y-x)\\\\(x)(y+x)(y-x)(x^2+y)](https://tex.z-dn.net/?f=y%5E2-x%5E2%3D%28y%2Bx%29%28y-x%29%5C%5C%5C%5C%28x%29%28y%2Bx%29%28y-x%29%28x%5E2%2By%29)
<h2>Answer:</h2>
In short, the factored form of this expression is:
![(x)(y+x)(y-x)(x^2+y)](https://tex.z-dn.net/?f=%28x%29%28y%2Bx%29%28y-x%29%28x%5E2%2By%29)
Your answer is 72 ounces
Problem: How many gallons were in the bowls at the start?
less the 34 cups they served during the first intermissionplus the amount the sixth-graders added, made after the first intermission (during the second act)less the quantity served during the second intermission
The result is the 2 gallons of punch at the end of the performance.
To find out how many gallons they had to begin with, work backward, starting with the 2 gallons left at the end of the performance. When working backward, reverse the operations that occurred in the story from beginning to end. Do this by following the steps below.
1) When finding a median, order your numerical list from smallest to larger, as so: 2,2,3,4,5,6,8,9.
2) Then start eliminating numbers from each side of the order; (The bolded numbers will be removed.)
2,2,3,4,5,6,8,9
2,3,4,5,6,8,9
2,3,4,5,6,8
3,4,5,6,8
3,4,5,6
4,5,6
4,5
3) Since there is an even number of digits in your list, you will have to add the last two digits and then divide them by two. 4 and 5 are the last numbers standing, (4+5=9)(9/2=4.5) and therefore your answer, would be 4.5, or B.