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) $$ \left(x^{2}+2 x+1\right)\left(x^{2}+3 x+4\right) $$

For Problems \(57-70\), find all real number solutions for each equation. (Objective 3) $$ 8 x^{2}-32=0 $$

The sum of the squares of two consecutive integers is 85 . Find the integers.

For Problems \(51-68\), factor by grouping. $$ 2 a c+3 b d+2 b c+3 a d $$

For Problems \(57-70\), simplify by removing the inner parentheses first and working outward. (Objective 3) $$ -7 n^{2}-\left[3 n^{2}-\left(-n^{2}-n+4\right)\right] $$

For Problems \(57-62\), factor completely each of the perfectsquare trinomials. (Objective 3 ) $$ 12 x^{2}+36 x+27 $$

The sum of the areas of two circles is \(65 \pi\) square feet. The length of a radius of the larger circle is 1 foot less than twice the length of a radius of the smaller circle. Find the length of a radius of each circle.

For Problems \(59-74\), find each quotient $$ \frac{56 x^{6} y^{4}}{-7 x^{2} y^{3}} $$

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) $$ \left(2 x^{2}+3 x-4\right)\left(x^{2}-2 x-1\right) $$

For Problems \(57-70\), find all real number solutions for each equation. (Objective 3) $$ 3 x^{2}-108=0 $$