Answer:
My answer to your question is a "No".
We can know that a and b are the same numbers. If we multiply the same number on each side, the answer will be the same. However, x and y have different values. So, it will show differently.
Let's have an example:
It we say a = 5, x = 6, y = 7.
We know a and b are the same number so, both a and b will be 5. If we multiply a by x, it will be 5 x 6 which is 30. It will show the same answer on multiplying b because as you said a and b are the same. The equation will be 5(a) x 6(x) = 5(b) x 6(x) Let's look at multiplying y. If we multiply a by y, it will be 5 x 7 which is 35. As you said it will show the same answer on multiplying b because a and b are the same. The equation for this will be 5(a) x 7(y) = 5(b) = 7(y). Finally, let's compare the two equations.
5(a) x 6(x) = 5(b) x 6(x) -> 30 = 30
5(a) x 7(y) = 5(b) = 7(y) -> 35 = 35
You can see it more clearly when we compare those to the equations that I made.
Thank you