Find the Quotient of 20x^2y-88xy/-4xy

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- anonymous

Find the Quotient of 20x^2y-88xy/-4xy

- chestercat

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- jim_thompson5910

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

- anonymous

Yes

- jim_thompson5910

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

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## More answers

- 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.

- jim_thompson5910

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

- jim_thompson5910

did you learn about factoring yet?

- anonymous

i believe so but I'm not positive

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

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

- jim_thompson5910

what do you mean?

- anonymous

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

- jim_thompson5910

have you learned about the distributive property?

- anonymous

is that not with (X)^Y

- jim_thompson5910

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

- anonymous

yeah i have

- jim_thompson5910

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

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

okay im some what following lol

- jim_thompson5910

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

- jim_thompson5910

|dw:1436404481447:dw|

- jim_thompson5910

|dw:1436404502668:dw|

- jim_thompson5910

|dw:1436404585098:dw|

- jim_thompson5910

|dw:1436404604417:dw|

- jim_thompson5910

|dw:1436404621090:dw|

- anonymous

why would it not be -8xy?

- jim_thompson5910

-8xy? where do you mean?

- anonymous

-4xy on both sides of the equation

- 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

- anonymous

okay so they two cancel one another out correct?

- jim_thompson5910

yeah they divide to 1 and go away effectively

- anonymous

okay i understand that

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