Chapter 5

Subtract using a vertical format. $$ \begin{array}{r} 5 x^{3}-4 x^{2}+6 x-2 \\ -\left(3 x^{3}-2 x^{2}-x-4\right) \\ \hline \end{array} $$

Simplify each expression. Write each result using positive exponents only. $$ \left(z^{5} x^{5}\right)^{-3} $$

The parallelogram below has base length \(9 y^{7}\) meters and height \(2 y^{10}\) meters. Find its area as an expression in \(y\).

Multiply. $$ (4 s-2 y)^{2} $$

Multiply. \((y-10)(y+11)\)

Add or subtract as indicated. $$ (3 x+5)+(2 x-14) $$

Mixed Practice Divide. If the divisor contains 2 or more terms, use long division. See Examples 1 through 8. $$ \frac{8 x^{2}+6 x-27}{2 x-3} $$

Simplify each expression by combining like terms. See Examples 6 through 10. $$ 8 s-5 s+4 s $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{\left(x^{2}\right)^{3}}{x^{10}} $$

Use the power rule and the power of a product or quotient rule to simplify eachexpression. $$ \left(x^{9}\right)^{4} $$

Multiply. $$ (4 m+5 n)^{2} $$

Multiply. \(\left(x+\frac{2}{3}\right)\left(x-\frac{1}{3}\right)\)

Add or subtract as indicated. $$ (2 y+20)+(5 y-30) $$

Simplify each expression by combining like terms. See Examples 6 through 10. $$ 5 y+7 y-6 y $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{\left(y^{4}\right)^{2}}{y^{12}} $$

Use the power rule and the power of a product or quotient rule to simplify each expression. $$ \left(y^{7}\right)^{5} $$

Multiply. $$ (3 n+5 m)^{2} $$

Multiply. \(\left(x+\frac{3}{5}\right)\left(x-\frac{2}{5}\right)\)

Add or subtract as indicated. $$ (9 x-1)-(5 x+2) $$

Simplify each expression by combining like terms. See Examples 6 through 10. $$ 0.1 y^{2}-1.2 y^{2}+6.7-1.9 $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{\left(a^{5}\right)^{2}}{\left(a^{3}\right)^{4}} $$

Use the power rule and the power of a product or quotient rule to simplify each expression. $$ (p q)^{8} $$

Multiply. $$ \left(5 x^{4}-3\right)^{2} $$

Multiply. \(\left(3 x^{2}+1\right)\left(4 x^{2}+7\right)\)

Add or subtract as indicated. $$ (7 y+7)-(y-6) $$

Simplify each expression by combining like terms. See Examples 6 through 10. $$ 7.6 y+3.2 y^{2}-8 y-2.5 y^{2} $$

Mixed Practice Divide. If the divisor contains 2 or more terms, use long division. See Examples 1 through 8. $$ \frac{11 x^{3} y^{3}-33 x y+x^{2} y^{2}}{11 x y} $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{\left(x^{2}\right)^{5}}{\left(x^{4}\right)^{3}} $$

Use the power rule and the power of a product or quotient rule to simplify each expression. $$ (a b)^{6} $$

Multiply. $$ \left(7 x^{3}-6\right)^{2} $$

Multiply. \(\left(5 x^{2}+2\right)\left(6 x^{2}+2\right)\)

Add or subtract as indicated. $$ (14 y+12)+(-3 y-5) $$

Mixed Practice Divide. If the divisor contains 2 or more terms, use long division. See Examples 1 through 8. $$ \frac{2 b^{3}+9 b^{2}+6 b-4}{b+4} $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{8 k^{4}}{2 k} $$

Use the power rule and the power of a product or quotient rule to simplify each expression. $$ \left(2 a^{5}\right)^{3} $$

Multiply. \((4 x-3)(3 x-5)\)

Add or subtract as indicated. $$ (26 y+17)+(-20 y-10) $$

Simplify each expression by combining like terms. See Examples 6 through 10. $$ \frac{2}{5} x^{4}-23 x^{2}+\frac{1}{15} x^{4}+5 x^{2}-5 $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{27 r^{6}}{3 r^{4}} $$

Use the power rule and the power of a product or quotient rule to simplify each expression. $$ \left(4 x^{6}\right)^{2} $$

Multiply. $$ (b+3)(b-3) $$

Multiply. \((8 x-3)(2 x-4)\)

Add or subtract as indicated. $$ \left(x^{2}+2 x+1\right)-\left(3 x^{2}-6 x+2\right) $$

Simplify each expression by combining like terms. See Examples 6 through 10. $$ \frac{3}{20} x^{3}+\frac{1}{10}-\frac{3}{10} x-\frac{1}{5}-\frac{7}{20} x+6 x^{2} $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{-6 m^{4}}{-2 m^{3}} $$

Use the power rule and the power of a product or quotient rule to simplify each expression. $$ \left(x^{2} y^{3}\right)^{5} $$

Multiply. $$ (x+6)(x-6) $$

Multiply. \((1-3 a)(1-4 a)\)

Add or subtract as indicated. $$ \left(5 y^{2}-3 y-1\right)-\left(2 y^{2}+y+1\right) $$

Simplify each expression by combining like terms. See Examples 6 through 10. $$ \frac{5}{16} x^{3}-\frac{1}{8}+\frac{3}{8} x+\frac{1}{4}-\frac{9}{16} x-14 x^{2} $$