Final answer:
To factorize the expression 2x² + 2x, we extract the common factor of 2x from both terms, which gives us 2x(x + 1) as the factorized form.
Step-by-step explanation:
To factorize the expression 2x² + 2x, we first look for common factors in both terms. Here, we can see that the number 2 and the variable x are common to both terms. So, we take 2x out as the common factor:
2x² + 2x = 2x(x + 1)
Factoring is the process of rewriting an expression as the product of its factors. In this case, the expression inside the parenthesis is (x + 1), and when multiplied back by 2x, gives us the original expression 2x² + 2x.
Therefore, the gap should be filled with 2x to factorize the expression completely.