Question 40949
This problem involves factoring by grouping terms together.

The first step is to find two nice groups containing like terms so that we can factor out the GCF.  Usually there will only be two groups of terms.

Try placing parenthesis around the first two terms and the second two terms.

  (2x^2+2xy)+(x+y)

Now, look for the GCF (greatest common factor) within each group.  Sometimes you may have to switch terms within groups until they have a GFC.

Next, factor out the GCF from each group.

The first group (2x^2+2xy)has a GCF of "2x".  So factor out the 2x. 
This will leave:
  (2x)(x+y) 

The second group (x+y) only has a GCF of "1". So factor out the 1.
This will leave:
  (1)(x+y)

Putting everything back together gives:

  (2x)(x+y)+ (1)(x+y)

Now,again factor out the GCF from the entire expression.  What does each term have in common?  What is the GCF?

The GCF is "(x+y)".  So after factoring out (x+y), group the remaining terms together to get the final answer.

  (x+y)(2x+1)

Check the answer by multiplying the factors using FOIL.
  (x+y)(2x+1)

  2x^2 + x + 2xy + y

Rearranging the terms:

  2x^2 + 2xy + x + y takes you back to the original expression.