Factorise 3a2+3ab−4a−4b completely.

Sure, here is the step-by-step solution:

Step 1: Group the terms that have common factors. In this case, we can group the first two terms and the last two terms together. This gives us:

(3a^2 + 3ab) - (4a + 4b)

Step 2: Factor out the common factors. For the first group, the common factor is 'a', and for the second group, the common factor is '4'. This gives us:

a(3a + 3b) - 4(a + b)

Step 3: Now, you can see that (3a + 3b) and (a + b) are similar. We can write 3b as b + 2b and 3a as a + 2a. This gives us:

a(a + 2a + b + 2b) - 4(a + b)

Step 4: Now, you can see that (a + b) is a common factor. So, we can factor that out. This gives us:

(a + b)(a + 2a - 4)

Step 5: Simplify the expression inside the second bracket. This gives us:

(a + b)(3a - 4)

So, the factorised form of 3a^2 + 3ab - 4a - 4b is (a + b)(3a - 4).