SOLUTION: How do you factor {{{4x^2 + 20x + 5y +xy}}}?

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Question 149833: How do you factor 4x%5E2+%2B+20x+%2B+5y+%2Bxy?
Found 3 solutions by jim_thompson5910, scott8148, Edwin McCravy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Well you can't solve it (since it's not an equation), but you can factor

4x%5E2%2B20x%2B5y%2Bxy Start with the given expression.


4x%5E2%2B20x%2Bxy%2B5y Rearrange the terms


%284x%5E2%2B20x%29%2B%28xy%2B5y%29 Group like terms


4x%28x%2B5%29%2By%28x%2B5%29 Factor out the GCF 4x out of the first group. Factor out the GCF y out of the second group


%284x%2By%29%28x%2B5%29 Since we have the common term x%2B5, we can combine like terms

So 4x%5E2%2B20x%2B5y%2Bxy factors to %284x%2By%29%28x%2B5%29

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
grouping __ (4x^2 + 20x) + (5y + xy)

factoring __ 4x(x+5) + y(5+x)

rearranging __ (4x+y)(x+5)

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
How do you factor 4x%5E2+%2B+20x+%2B+5y+%2Bxy? 

By grouping, factor 4x out of the first two terms only:

4x%28x+%2B+5%29+%2B+5y+%2Bxy

Next factor y out of the last two terms only:

4x%28x+%2B+5%29+%2B+y%285+%2Bx%29
 
Notice that %28x%2B5%29 is the same as %285%2Bx%29,
so we write %285%2Bx%29 as %28x%2B5%29 

4x%28x+%2B+5%29+%2B+y%28x%2B5%29

Now the %28x%2B5%29 is a common factor. So we factor it
out as:

%28x+%2B+5%29%284x%2By%29

Edwin