Chapter 6

factor the given expressions completely. $$x^{3}+1$$

factor the given expressions completely. $$R^{3}+27$$

Perform the indicated operations and simplify. $$\frac{3}{5}+\frac{6}{5}$$

Solve the given equations and check the results. $$\frac{x}{2}+6=2 x$$

In Exercises \(5-12,\) multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. $$\frac{2}{3} \quad(b y 7)$$

Perform the indicated operations and simplify. For Exercises \(33,34,39,\) and \(40,\) check the solution with a graphing calculator. $$\frac{3}{5}+\frac{6}{5}$$

factor the given expressions completely. $$8-t^{3}$$

Simplify the given expressions involving the indicated multiplications and divisions. $$\frac{3}{8} \times \frac{2}{7}$$

Multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. $$\left.\frac{2}{3} \quad \text { (by } 7\right)$$

Find the indicated products directly by inspection. It should not be necessary to write down intermediate steps [except possibly when using Eq. (6.6) ] $$40(x-y)$$

Factor the given expressions completely. $$6 x+6 y$$

Perform the indicated operations and simplify. $$\frac{2}{13}+\frac{6}{13}$$

Solve the given equations and check the results. $$\frac{x}{5}+2=\frac{15+x}{10}$$

In Exercises \(5-12,\) multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. $$\frac{7}{5}(\text { by } 9)$$

Perform the indicated operations and simplify. For Exercises \(33,34,39,\) and \(40,\) check the solution with a graphing calculator. $$\frac{2}{13}+\frac{6}{13}$$

factor the given expressions completely. $$8 r^{3}-1$$

Simplify the given expressions involving the indicated multiplications and divisions. $$11 \times \frac{13}{33}$$

Multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. $$\frac{7}{5} \text { (by } 9 \text { ) }$$

Find the indicated products directly by inspection. It should not be necessary to write down intermediate steps [except possibly when using Eq. (6.6) ] $$2 x(a-3)$$

Factor the given expressions completely. $$3 a-3 b$$

Factor the given expressions completely. $$x^{2}+5 x+4$$

Perform the indicated operations and simplify. $$\frac{1}{x}+\frac{7}{x}$$

Solve the given equations and check the results. $$\frac{x}{6}-\frac{1}{2}=\frac{x}{3}$$

In Exercises \(5-12,\) multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. $$\frac{a x}{y} \quad(\text { by } 2 x)$$

Perform the indicated operations and simplify. For Exercises \(33,34,39,\) and \(40,\) check the solution with a graphing calculator. $$\frac{1}{x}+\frac{7}{x}$$

Simplify the given expressions involving the indicated multiplications and divisions. $$\frac{4 x}{3 y} \times \frac{9 y^{2}}{2}$$

factor the given expressions completely. $$27 x^{3}-8 a^{6}$$

Find the indicated products directly by inspection. It should not be necessary to write down intermediate steps [except possibly when using Eq. (6.6) ] $$2 x^{2}(x-4)$$

Factor the given expressions completely. $$5 a-5$$

Factor the given expressions completely. $$x^{2}-5 x-6$$

Perform the indicated operations and simplify. $$\frac{2}{a}+\frac{3}{a}$$

Solve the given equations and check the results. $$\frac{3 N}{8}-\frac{3}{4}=\frac{N-4}{2}$$

In Exercises \(5-12,\) multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. $$\frac{2 x^{2} y}{3 n} \quad\left(\text { by } 2 x n^{2}\right)$$

Perform the indicated operations and simplify. For Exercises \(33,34,39,\) and \(40,\) check the solution with a graphing calculator. $$\frac{2}{a}+\frac{3}{a}$$

factor the given expressions completely. $$64 x^{4}+125 x$$

Simplify the given expressions involving the indicated multiplications and divisions. $$\frac{18 s y^{3}}{a x^{2}} \times \frac{(a x)^{2}}{3 s}$$

Multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. $$\frac{2 x^{2} y}{3 n} \quad\left(\text { by } 2 x n^{2}\right)$$

Find the indicated products directly by inspection. It should not be necessary to write down intermediate steps [except possibly when using Eq. (6.6) ] $$3 a^{2}(2 a+7)$$

Factor the given expressions completely. $$2 x^{2}+2$$

Factor the given expressions completely. $$s^{2}-s-42$$

Perform the indicated operations and simplify. $$\frac{1}{2}+\frac{3}{4}$$

Solve the given equations and check the results. $$1-\frac{t-5}{6}=\frac{3}{4}$$

In Exercises \(5-12,\) multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. $$\frac{2}{x+3}(\text { by } x-2)$$

Perform the indicated operations and simplify. For Exercises \(33,34,39,\) and \(40,\) check the solution with a graphing calculator. $$\frac{1}{2}+\frac{3}{4}$$

Simplify the given expressions involving the indicated multiplications and divisions. $$\frac{2}{9} \div \frac{4}{7}$$

factor the given expressions completely. $$4 x^{3}+32$$

Multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. $$\frac{2}{x+3} \quad(\text { by } x-2)$$

Find the indicated products directly by inspection. It should not be necessary to write down intermediate steps [except possibly when using Eq. (6.6) ] $$(T+6)(T-6)$$

Factor the given expressions completely. $$3 x^{2}-9 x$$

Factor the given expressions completely. $$a^{2}+14 a-32$$