Chapter 5

Multiply. \(-2 a(a+4)\)

Subtract. $$ (4+5 a)-(-a-5) $$

Simplify each expression. Write each result using positive exponents only. $$ 4^{-2}-4^{-3} $$

Evaluate each expression with the given replacement values. $$ -4 x^{2} y^{3} \text { when } x=2 \text { and } y=-1 $$

Multiply using the FOIL method. See Examples 1 through 3. $$ (x+4 y)(3 x-y) $$

Multiply. \(-3 a(2 a+7)\)

Subtract. $$ \left(5 x^{2}+4\right)-\left(-2 y^{2}+4\right) $$

A rocket is fired upward from the ground with an initial velocity of 200 feet per second. Neglecting air resistance, the height of the rocket at any time t can be described in feet by the polynomial \(-16 t^{2}+200 t\). Find the height of the rocket at the time given in Exercises 19 through 22. See Example 5. $$ \begin{array}{c|c} \text { Time, } \boldsymbol{t} & \text { Height } \\ \text { (in seconds) } & -16 t^{2}+200 t \\ \hline 1 & \\ \hline \end{array} $$

Simplify each expression. Write each result using positive exponents only. $$ (-3)^{-2} $$

Evaluate each expression with the given replacement values. $$ \frac{2 z^{4}}{5} \text { when } z=-2 $$

Multiply. \(3 x\left(2 x^{2}-3 x+4\right)\)

Subtract. $$ \left(-7 y^{2}+5\right)-\left(-8 y^{2}+12\right) $$

Simplify each expression. Write each result using positive exponents only. $$ (-2)^{-6} $$

Multiply. $$ (x+7)^{2} $$

Evaluate each expression with the given replacement values. $$ \frac{10}{3 y^{3}} \text { when } y=-3 $$

Multiply. \(4 x\left(5 x^{2}-6 x-10\right)\)

Subtract. $$ 3 x-(5 x-9) $$

A rocket is fired upward from the ground with an initial velocity of 200 feet per second. Neglecting air resistance, the height of the rocket at any time t can be described in feet by the polynomial \(-16 t^{2}+200 t\). Find the height of the rocket at the time given in Exercises 19 through 22. See Example 5. $$ \begin{array}{c|c} \text { Time, } \boldsymbol{t} & \text { Height } \\ \text { (in seconds) } & -16 t^{2}+200 t \\ \hline 7.6 & \\ \hline \end{array} $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{-1}{p^{-4}} $$

Use the product rule to simplify each expression. $$ x^{2} \cdot x^{5} $$

Multiply. $$ (2 a-3)^{2} $$

Multiply. \(3 a^{2}\left(4 a^{3}+15\right)\)

Subtract. $$ 4-(-y-4) $$

A rocket is fired upward from the ground with an initial velocity of 200 feet per second. Neglecting air resistance, the height of the rocket at any time t can be described in feet by the polynomial \(-16 t^{2}+200 t\). Find the height of the rocket at the time given in Exercises 19 through 22. See Example 5. $$ \begin{array}{c|c} \text { Time, } \boldsymbol{t} & \text { Height } \\ \text { (in seconds) } & -16 t^{2}+200 t \\ \hline 10.3 & \\ \hline \end{array} $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{-1}{y^{-6}} $$

Multiply. $$ (7 x-3)^{2} $$

Use the product rule to simplify each expression. $$ y^{2} \cdot y $$

Multiply. \(9 x^{3}\left(5 x^{2}+12\right)\)

Subtract. $$ \left(2 x^{2}+3 x-9\right)-(-4 x+7) $$

Find each quotient using long division. See Examples 4 and 5. $$ \frac{2 x^{3}+2 x^{2}-17 x+8}{x-2} $$

The polynomial \(-7.5 x^{2}+93 x-100\) models the yearly number of visitors (in thousands) \(x\) years after 2000 at Apostle Islands National Park. Use this polynomial to estimate the number of visitors to the park in \(2008(x=8)\).

Simplify each expression. Write each result using positive exponents only. $$ -2^{0}-3^{0} $$

Multiply. $$ (3 a-5)^{2} $$

Use the product rule to simplify each expression. $$ (-3)^{3} \cdot(-3)^{9} $$

Multiply. \(-2 a^{2}\left(3 a^{2}-2 a+3\right)\)

Subtract. $$ \left(-7 x^{2}+4 x+7\right)-(-8 x+2) $$

The polynomial \(8 x^{2}-90.6 x+752\) models the yearly number of visitors (in thousands) \(x\) years after 2000 at Cedar Breaks National Park. Use this polynomial to estimate the number of visitors to the park in \(2007(x=7)\)

Simplify each expression. Write each result using positive exponents only. $$ 5^{0}+(-5)^{0} $$

Multiply. $$ (5 a-2)^{2} $$

Use the product rule to simplify each expression. $$ (-5)^{7} \cdot(-5)^{6} $$

Multiply. \(-4 b^{2}\left(3 b^{3}-12 b^{2}-6\right)\)

Subtract. $$ (5 x+8)-\left(-2 x^{2}-6 x+8\right) $$

Find each quotient using long division. Don't forget to write the polynomials in descending order and fill in any missing terms. See Examples 6 through 8. $$ \frac{x^{2}-36}{x-6} $$

The number of wireless telephone subscribers (in millions) \(x\) years after 1995 is given by the polynomial \(0.52 x^{2}+11.4 x+27.87\) for 1995 through 2008\. Use this model to predict the number of wireless telephone subscribers in \(2012(x=17)\) (Source: Based on data from Cellular Telecommunications \& Internet Association)

Simplify each expression. Write each result using positive exponents only. $$ \frac{x^{2} x^{5}}{x^{3}} $$

Multiply. $$ \left(x^{2}+0.5\right)^{2} $$

Use the product rule to simplify each expression. $$ \left(5 y^{4}\right)(3 y) $$

Multiply. \(3 x^{2} y\left(2 x^{3}-x^{2} y^{2}+8 y^{3}\right)\)

Subtract. $$ \left(-6 y^{2}+3 y-4\right)-\left(9 y^{2}-3 y\right) $$

Find each quotient using long division. Don't forget to write the polynomials in descending order and fill in any missing terms. See Examples 6 through 8. $$ \frac{a^{2}-49}{a-7} $$