1. **Problem statement:** Simplify the expression \((x^3+x^2y+xy^2+y^3)(x+y)-2x^3y-3x^2y^2-2xy^3\) and then calculate its value at \(x=-1\) and \(y=-1\). 2. **Formula and rules:** Use distributive property to expand products and combine like terms. 3. **Step-by-step simplification:** \[(x^3+x^2y+xy^2+y^3)(x+y) = x^3(x+y) + x^2y(x+y) + xy^2(x+y) + y^3(x+y)\] Expanding each term: \[= x^4 + x^3y + x^3y + x^2y^2 + x^2y^2 + xy^3 + xy^3 + y^4\] Combine like terms: \[= x^4 + 2x^3y + 2x^2y^2 + 2xy^3 + y^4\] Now subtract the remaining terms: \[x^4 + 2x^3y + 2x^2y^2 + 2xy^3 + y^4 - 2x^3y - 3x^2y^2 - 2xy^3\] Simplify by canceling terms: \[= x^4 + \cancel{2x^3y} + 2x^2y^2 + \cancel{2xy^3} + y^4 - \cancel{2x^3y} - 3x^2y^2 - \cancel{2xy^3}\] \[= x^4 + (2x^2y^2 - 3x^2y^2) + y^4 = x^4 - x^2y^2 + y^4\] 4. **Calculate value at \(x=-1, y=-1\):** \[(-1)^4 - (-1)^2(-1)^2 + (-1)^4 = 1 - 1 + 1 = 1\] **Final answer:** \[\boxed{x^4 - x^2y^2 + y^4}\] Value at \(x=-1, y=-1\) is \(1\).