Factorise w2−30w+225 completely.

Sure, here are the steps to factorise the given expression:

1. Identify the expression: w^2 - 30w + 225

2. Look for two numbers that multiply to 225 (the last term) and add up to -30 (the coefficient of the middle term). The numbers that satisfy these conditions are -15 and -15.

3. Rewrite the middle term of the expression as the sum of the terms -15w and -15w: w^2 - 15w - 15w + 225

4. Factor by grouping: w(w - 15) - 15(w - 15)

5. Notice that (w - 15) is a common factor: (w - 15)(w - 15)

6. So, the factorised form of the expression w^2 - 30w + 225 is (w - 15)^2.