## anonymous one year ago Find the Quotient of 20x^2y-88xy/-4xy

1. jim_thompson5910

The problem is this, right? $\Large \frac{20x^2y-88xy}{-4xy}$

2. anonymous

Yes

3. jim_thompson5910

we can factor out -4xy from the numerator $\Large \frac{20x^2y-88xy}{-4xy} = \frac{-4xy(-5x+22)}{-4xy}$ what comes next?

4. anonymous

I'm having a very hard time understanding even from the beginning, if you can i would love for you to help explain it to me.

5. jim_thompson5910

well I factored out -4xy because that's what is in the denominator I want to cancel out the denominator

6. jim_thompson5910

did you learn about factoring yet?

7. anonymous

i believe so but I'm not positive

8. jim_thompson5910

the idea of factoring is to rewrite a number or expression as a product of two smaller things

9. jim_thompson5910

ex: 27 = 9*3 16 = 8*2

10. anonymous

could possibly be 22x^2y^2+20x^2y

11. jim_thompson5910

what do you mean?

12. anonymous

for the awnser i asked my mom and she said she thinks that is what it is

13. jim_thompson5910

have you learned about the distributive property?

14. anonymous

is that not with (X)^Y

15. jim_thompson5910

it's something like 2*(x+y) = 2*x + 2*y

16. anonymous

yeah i have

17. jim_thompson5910

so when I factored back up at the top, I used the distributive property (in reverse)

18. jim_thompson5910

if you have 2*x + 2*y you can factor out 2 to get 2*(x+y)

19. jim_thompson5910

same idea with your problem, but I pulled out -4xy

20. anonymous

okay im some what following lol

21. jim_thompson5910

it turns out that -4xy is a common factor of 20x^2y and -88xy

22. jim_thompson5910

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23. jim_thompson5910

|dw:1436404502668:dw|

24. jim_thompson5910

|dw:1436404585098:dw|

25. jim_thompson5910

|dw:1436404604417:dw|

26. jim_thompson5910

|dw:1436404621090:dw|

27. anonymous

why would it not be -8xy?

28. jim_thompson5910

-8xy? where do you mean?

29. anonymous

-4xy on both sides of the equation

30. jim_thompson5910

I'm not sure what you mean exactly, but this is what the full step by step picture looks like $\Large \frac{20x^2y-88xy}{-4xy} = \frac{-4xy(-5x+22)}{-4xy}$ $\Large \frac{20x^2y-88xy}{-4xy} = \frac{\cancel{-4xy}(-5x+22)}{\cancel{-4xy}}$ $\Large \frac{20x^2y-88xy}{-4xy} = -5x+22$ so the original expression simplifies to -5x+22

31. anonymous

okay so they two cancel one another out correct?

32. jim_thompson5910

yeah they divide to 1 and go away effectively

33. anonymous

okay i understand that