1. The problem is to expand the expression $a^2 + b^2 - 3ab(a + b)$.\n2. First, distribute $-3ab$ over $(a + b)$ using the distributive property: $-3ab \times a = -3a^2b$ and $-3ab \times b = -3ab^2$.\n3. So the expression becomes: $$a^2 + b^2 - 3a^2b - 3ab^2$$\n4. This is the expanded form; there are no like terms to combine further.\n5. To summarize, the steps are:\n\n- Start with $a^2 + b^2 - 3ab(a + b)$\n- Distribute: $a^2 + b^2 - 3a^2b - 3ab^2$\n\nFinal answer: $$a^2 + b^2 - 3a^2b - 3ab^2$$