Factorise 4x2+4xy−5x−5y completely.

Sure, let's factorise the given expression step by step:

The given expression is 4x² + 4xy - 5x - 5y.

Step 1: Group the terms to make it easier to factorise.

We can group the terms as follows: (4x² + 4xy) - (5x + 5y).

Step 2: Factor out the common factors in each group.

In the first group, the common factor is 4x, and in the second group, the common factor is 5. So, we get:

4x(x + y) - 5(x + y).

Step 3: Notice that (x + y) is a common factor in both terms.

So, we can factor out (x + y) to get:

(4x - 5)(x + y).

So, the expression 4x² + 4xy - 5x - 5y factorises to (4x - 5)(x + y).