2. Find the product of following: \( \begin{array}{ll}\text { (a) }\left(x^{3}-4 x+8\right)(3 x+4) & \text { (b) }\left(-x^{2}-3 x+9\right)(-4 x-7) \\ \text { (c) }\left(9 x^{2}-x+15\right)\left(x^{3}-5\right) & \text { (d) }\left(x^{2}-2 x y-y^{2}\right)(x+y) \\ \text { (e) }\left(x^{2}-x y+y^{2}\right)(x+y) & \text { (f) }\left(x^{2}-2 x y+y^{2}\right)(x-y) \\ \text { (g) }(2 x+3 y-5)(x-y+2) & \text { (h) }\left(x^{2}+x y+y^{2}\right)(x-y) \\ \text { (i) }\left(\frac{5}{4} x^{3}-\frac{7}{6} x^{2}+\frac{3}{2} x\right)(x+y) & \text { (j) }\left(-2 x^{2}-3 x-7\right)\left(-3 x^{2}-5 x-4\right) \\ \text { (k) }\left(x^{2}-5 x+18\right)\left(x^{2}+2 x-13\right) & \end{array} \)

Three-fifths of Jesse Black's inventory was destroyed by fire. He sold the remaining part, which was slightly damaged, for two-thirds of its value and received \( \$ 3400 \). (a) What was the value of the destroyed part of the inventory? (b) What was the value of the inventory before the fire? (a) The value is \( \$ \square \). (Round to the nearest cent as needed.)

Rewrite the following without an exponent \[ (-7)^{-2} \]

Calcule todos los valores de a para los cuales la matriz \( A=\left[\begin{array}{lll}a & 0 & 4 \\ 1 & 1 & a \\ a & 1 & 2\end{array}\right] \) es no invertit

\begin{tabular}{l|l}\( \begin{array}{l}\text { Simplify the expression so that no negative exponents } \\ \text { appear in the final result. Assume all variables represent } \\ \text { nonzero real numbers. }\end{array} \) & \( \begin{array}{l}\left(4 a^{-2}\right)^{4}\left(a^{4}\right)^{-3}=\square \\ \\ \left(4 a^{-2}\right)^{4}\left(a^{4}\right)^{-3}\end{array} \) \\ exponents only.) \end{tabular}

Simplify. \( [32-(15+5) \div 4]-[56 \div(8-1)]^{\prime} \) \( [32-(15+5) \div 4]-[56 \div(8-1)]=\square \)