1. **State the problem:** Simplify the expression $$2(a + b)^2 - x(a + b)$$. 2. **Recall the formulas:** - Square of a binomial: $$(a + b)^2 = a^2 + 2ab + b^2$$ - Distributive property: $$x(y + z) = xy + xz$$ 3. **Expand the square:** $$2(a + b)^2 = 2(a^2 + 2ab + b^2) = 2a^2 + 4ab + 2b^2$$ 4. **Expand the second term:** $$x(a + b) = xa + xb$$ 5. **Rewrite the original expression:** $$2a^2 + 4ab + 2b^2 - (xa + xb)$$ 6. **Distribute the minus sign:** $$2a^2 + 4ab + 2b^2 - xa - xb$$ 7. **Final simplified expression:** $$\boxed{2a^2 + 4ab + 2b^2 - xa - xb}$$ This is the simplified form of the given expression. No like terms can be combined further because the variables differ.