1. The first expression given is $2x - x^2 + 2xy - xy^2$. 2. The second expression to expand and simplify is $(x + a)(x + b) - (x - a)(x - b)$. 3. Let's expand each product: - $(x + a)(x + b) = x^2 + (a + b)x + ab$ - $(x - a)(x - b) = x^2 - (a + b)x + ab$ 4. Now subtract the second from the first: $$ (x + a)(x + b) - (x - a)(x - b) = [x^2 + (a + b)x + ab] - [x^2 - (a + b)x + ab] $$ 5. Simplify by removing brackets: $$ x^2 + (a + b)x + ab - x^2 + (a + b)x - ab $$ 6. Combine like terms: $$ (a + b)x + (a + b)x = 2(a + b)x $$ 7. So the simplified form is: $$ 2(a + b)x $$ 8. Regarding your attempt on paper, the expression you wrote for $(x - y)^2$ is incorrect. The correct expansion is: $$ (x - y)^2 = x^2 - 2xy + y^2 $$ 9. Your attempt includes extra terms and does not match the standard binomial expansion. 10. Therefore, your attempt is incorrect compared to the standard formula. Final answers: - Simplified expression: $2(a + b)x$ - Correct expansion of $(x - y)^2$: $x^2 - 2xy + y^2$