Final answer:
The expression mx + cx + my + cy is factorised by finding common factors and grouping terms. The fully factorised form is (m + c)(x + y).
Step-by-step explanation:
To factorise the expression mx + cx + my + cy fully, we should look for common factors in each term. We can observe that 'x' is a common factor in the first two terms and 'y' is a common factor in the last two terms. By grouping the terms, we can rewrite the expression as (mx + cx) + (my + cy), and then factor out the common factors from each group.
Factoring out 'x' from the first group gives us x(m + c). Similarly, factoring out 'y' from the second group gives us y(m + c). Now, as (m + c) is common in both terms, we can factor it out to give us the final factored form of the expression:
(m + c)(x + y)
So the fully factorised form of the expression mx + cx + my + cy is (m + c)(x + y).