For a certain reaction, the rate = k [ A ] ^ 2 [ B ] , when the...

The rate law is : rate = (k[A]^2 \left[B\right])...(1)

The rate of the reaction when the concentration of A is Trippled and B is kept constant:

${r}_{1} = k{\left[3A\right]}^{2}\left[B\right]$

${r}_{1} = 9k{\left[A\right]}^{2}\left[B\right]$.....(2)

From equation first and second:

${r}_{1} = 9r$

Thus, the rate is increased by a factor of 9.