Appendix A - Review - A.3 Polynomials - A.3 Assess Your Understanding - Page A29: 3

$x^{3}-8$

Distribute: $(x-2)(x^{2}+2x+4)\\ =x(x^{2}+2x+4)-2(x^{2}+2x+4)$ $=x^{3}+2x^{2}+4x-2x^{2}-4x-8$ Combine like terms: $=x^{3}-8$ ALTERNATIVELY: We could have recognized the formula for the difference of cubes $A^{3}-B^{3}=(A-B)(A^{2}+AB+B^{2})$ with $A=x \text{ and } B=2$