Question 362058
I need to find the quotient and show all work 

{{{(64x^2 - 100y^2)/(8x + 10y)}}} 

This is what I have

{{{(64x^2)/(8x) = 8x}}}

{{{(-100y^2)/(10y) = -10y}}}

Is this correct? 
<pre>
No that's wrong.  You can't break up added or subtracted terms
in the numerator and denominator of a fraction the same way as 
you can break up factors in the numerator and denominator of a
fraction.

You can do this either of 2 ways:

1.  By factoring and canceling:

{{{(64x^2 - 100y^2)/(8x + 10y)}}}

Factor 4 out of top
Factor 2 out of the bottom:

{{{(4(16x^2 - 25y^2))/(2(4x + 5y))}}}

Cancel the 2 into the 4

 {{{2}}}
{{{(cross(4)(16x^2 - 25y^2))/(cross(2)(4x + 5y))}}}

{{{(2(16x^2 - 25y^2))/((4x + 5y))}}}

Factor the parenthetical expression in the top as the 
difference of two squares.

{{{(2(4x-5y)(4x+5y))/((4x+5y))}}}

Cancel the {{{(4x+5y)}}}'s

{{{(2(4x-5y)(cross(4x+5y)))/((cross(4x+5y)))}}}

All that's left is {{{2(4x-5y)}}}

And you can multiply that out as

          8x - 10y

--------------------------------

</pre>
Can this be solved using long division. I tried that way but it doesn't come out right. I appreciate any help you can give me  Thank you!
<pre>

2.  Yes, it can also be done by long division:

{{{(64x^2 - 100y^2)/(8x + 10y)}}}

We insert a zero term in xy in the numerator:

{{{(64x^2 +0xy- 100y^2)/(8x + 10y)}}}

        <u>          8x -  10y</u>
8x + 10y)64x² +  0xy - 100y²
         <u>64x² + 80xy</u> 
               -80xy - 100y²  
               <u>-80xy - 100y²</u>

So the answer is the same

          8x - 10y
               
Edwin</pre>