91Ó°ÊÓ

Factor each perfect square trinomial completely. $$9 m^{2} n^{2}-12 m n+4$$

Find each product or quotient. $$\frac{x^{3}+y^{3}}{x^{3}-y^{3}} \cdot \frac{x^{2}-y^{2}}{x^{2}+2 x y+y^{2}}$$

Perform the indicated operations. Write your answers with only positive exponents. Assume that all variables represent positive real numbers. $$\left(4 a^{-2} b^{7}\right)^{1 / 2} \cdot\left(2 a^{1 / 4} b^{3}\right)^{5}$$

Find each product or quotient. $$\frac{x^{2}-y^{2}}{(x-y)^{2}} \cdot \frac{x^{2}-x y+y^{2}}{x^{2}-2 x y+y^{2}} \div \frac{x^{3}+y^{3}}{(x-y)^{4}}$$

If possible, simplify each radical expression. Assume that all variables represent positive real numbers. $$\sqrt{24 m^{6} n^{5}}$$

Perform the indicated operations. Write your answers with only positive exponents. Assume that all variables represent positive real numbers. $$\left(x^{-2} y^{1 / 3}\right)^{5} \cdot\left(8 x^{2} y^{-2}\right)^{-1 / 3}$$

Factor each perfect square trinomial completely. $$(a-3 b)^{2}-6(a-3 b)+9$$

In words, state the formula for the product of the sum and difference of two terms.

Which of these rational expressions equal \(-1 ?\) (Assume that all denominators are nonzero. A. \(\frac{x-4}{x+4} \quad\) B. \(\frac{-x-4}{x+4}\) C. \(\frac{x-4}{4-x} \quad\) D. \(\frac{x-4}{-x-4}\)

Perform the indicated operations. Write your answers with only positive exponents. Assume that all variables represent positive real numbers. $$\left(\frac{r^{-2}}{s^{-5}}\right)^{-3}$$