91Ó°ÊÓ

For Problems \(1-74\), find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. (Objectives 1-4) $$ (2 x+3)^{3} $$

For Problems \(57-70\), simplify by removing the inner parentheses first and working outward. (Objective 3) $$ \left[4 x^{3}-\left(2 x^{2}-x-1\right)\right]-\left[5 x^{3}-\left(x^{2}+2 x-1\right)\right] $$

For Problems \(59-74\), find each quotient $$ \frac{-72 x^{2} y^{4}}{-8 x^{2} y^{4}} $$

For Problems \(57-70\), find all real number solutions for each equation. (Objective 3) $$ 6 x^{3}+24 x=0 $$

The area of a triangular sheet of paper is 28 square inches. One side of the triangle is 2 inches more than three times the length of the altitude to that side. Find the length of that side and the altitude to the side.

For Problems \(57-70\), find all real number solutions for each equation. (Objective 3) $$ 4 x^{3}+12 x=0 $$

For Problems \(1-74\), find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. (Objectives 1-4) $$ (3 x+1)^{3} $$

For Problems \(59-74\), find each quotient $$ \frac{-96 x^{4} y^{5}}{12 x^{4} y^{4}} $$

Problems \(63-100\) should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. (Objective 4) $$ (x+5)^{2}-y^{2} $$

For Problems \(57-70\), simplify by removing the inner parentheses first and working outward. (Objective 3) $$ \left[x^{3}-\left(x^{2}-x+1\right)\right]-\left[-x^{3}+\left(7 x^{2}-x+10\right)\right] $$