Factorise a2+ab−24a−24b completely.

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

The given expression is a² + ab - 24a - 24b.

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

a² + ab - 24a - 24b = (a² - 24a) + (ab - 24b)

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

= a(a - 24) + b(a - 24)

Step 3: Notice that (a - 24) is a common factor.

= (a + b)(a - 24)

So, a² + ab - 24a - 24b factorises to (a + b)(a - 24).