Factor completely, then place the factors in the proper location on the grid. 2a2 + 2b2 - 5ab

For this case we have the following expression:
  
 Rewriting the expression we have:
  
 From here, we factor the expression completely.
 We have then:
  
 Let's check the factorization.
 To do this, we multiply the terms within the parenthesis.
 We have then:
 
 Rewriting:
  
 Therefore, the factorization is correct.
 
  

Factored form is (2a-b)(a-2b).

Explanation:
To factor this, we can first write it as 2a²-5ab+2b².

We want factors of 2a²(2b²)=4a²b² that sum to -5ab. -4ab(-1ab) = 4a²b², and -4ab+-1ab = -5ab, so that is what we will use. This is how we will "split up" the middle term:
2a²-4ab-1ab+2b².

We group together the first two terms and the last two terms:
(2a²-4ab)+(-1ab+2b²).

Factor out the GCF of each group. The GCF of the first group is 2a: 2a(a-2b). The GCF of the second group is -1b: -1b(a-2b).

These two now have another common factor, (a-2b). We factor this out and get our answer, (a-2b)(2a-b).