Step-by-step explanation
The rate law depends on coefficients in the rate-determining step of this reaction (the slowest step). The equation A + 2 B → C represents the overall reaction. Finding the rate law requires experimental data. 
Compare row 1 and row 2:
- [A]₀ is the same in row 2 and row 1;
 - [B]₀ is twice as much in row 2 as in row 1;
 - Rate of change in [C] is four times as much in row 2 as in row 1.
 
- 2² = 4. As a result, the reaction is of second order with respect to B.
 
Compare row 1 and row 3:
- [A]₀ is twice as much in row 3 as in row 1;
 - [B]₀ is the same in row 3 and row 1;
 - Rate of change in [C] is twice as much in row 3 as in row 1.
 
- 2¹ = 2. As a result, the reaction is of first order with respect to A.
 
What would be the rate law of this reaction?
Rate = k · [A] · [B]².