1)(x+y)(x^2-xy+y^2) = x^3+y^3
2)(x+y)(x^3-x^2y+xy^-y^3) = x^4 - x^3y + x^2y^2 - xy^3 + x^3y - x^2y^2 + xy^3 - y^4 = x^4 - y^4
3)(x^3+2x+1)(x^2-X-1) = x^5 + x^4 - x^3 + 2x^4 + 2x^3 - 2x^2 + x^2 - 1 = x^5 + 3x^4 + x^3 - x^2 + x -1
4)(a^3+3a^2+a+1)(a^2+2a-1) = a^5 + 2a^4 - a^3 + 3a^4 + 6a^3 - 3a^2 + a^3 + 2a^2 - a + a^2 + 2a - 1 = a^5 + 5a^4 + 6a^3 + a - 1
5)(b^4+3b^3+b+2)(b^3-b^2+1) = b^7 - b^6 + b^4 + 3b^6 - 3b^5 + 3b^3 + b^4 - b^3 + b + 2b^3 - 2b^2 + 2 = b^7 + 2b^6 + 2b^4 - 3b^5 + 4b^3 + b - 2b^2 + 2
6)(a^2+a+1)(a^3+a^2-1) = a^5 + a^4 - a^2 + a^4 + a^3 - a + a^3 + a^2 - 1 = a^5 + 2a^4 + 2a^3 - a -1