Chapter 1 - Section 1.3 - Algebraic Expressions - 1.3 Exercises - Page 35: 142

(a) $(A-B)\times(A^{2}+AB+B^{2})=A^{3}-B^{3}$ (b)$(A+B)\times(A^{2}-AB+B^{2})=A^{3}+B^{3}$

(a) $(A-B)\times(A^{2}+AB+B^{2})=A^{3}+A^{2}B+AB^{2}-(A^{2}B+AB^{2}+B^{3})=A^{3}+A^{2}B+AB^{2}-A^{2}B-AB^{2}-B^{3}=A^{3}-B^{3}$ (b)$(A+B)\times(A^{2}-AB+B^{2})=A^{3}-A^{2}B+AB^{2}+A^{2}B-AB^{2}+B^{3}=A^{3}+B^{3}$