To simplify this expression, we can use the trigonometric identity for the cosine of the sum of two angles:

cos(A + B) = cos A cos B - sin A sin B

In this case, our expression is:

cos(3a)cos(a) - sin(a)sin(3a)

We can use the angle addition formula for the cosine to expand this expression:

cos(A + B) = cos A cos B - sin A sin B

cos(3a)cos(a) - sin(a)sin(3a) = cos(3a + a)

Now, simplifying the expression inside the cosine function:

3a + a = 4a

So, the simplified expression becomes:

cos(4a)