Chapter 1

Perform the indicated operations and simplify. $$ (0.2 x+1.2 y)(0.3 x-2.1 y) $$

Perform the indicated operations and simplify. \(\frac{2 x+1}{2 x^{2}-x-1}-\frac{x+1}{2 x^{2}+3 x+1}+\frac{4}{x^{2}+2 x-3}\)

Evaluate the expression. $$ |\pi-6|-3 $$

Solve the equation by using the quadratic formula. $$ 0.2 m^{2}+1.6 m+1.2=0 $$

Carry out the indicated operation and write your answer using positive exponents only. $$ \left(\frac{r^{n}}{r^{5-2 n}}\right)^{4} $$

Simplify the expression, writing your answer using positive exponents only. $$ \left(2^{-1} r^{3}\right)^{-2}\left(3 s^{-1}\right)^{2} $$

Solve the given equation. $$ \sqrt{4 k^{2}-3}=2 k+1 $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 2 x(x+y)^{2}-8 x\left(x+y^{2}\right)^{2} $$

State the real number property that iustifies the statement $$ \frac{x+y}{x+1}-\frac{y}{x}=\frac{x^{2}-y}{x(x+1)} $$

Perform the indicated operations and simplify. $$ (3.2 m-1.7 n)(4.2 m+1.3 n) $$

Perform the indicated operations and simplify. \(\frac{x}{a x-a y}+\frac{y}{b y-b x}\)

Evaluate the expression. $$ |\sqrt{2}-1|+|3-\sqrt{2}| $$

Solve the equation. $$ x^{4}-5 x^{2}+6=0 $$

Carry out the indicated operation and write your answer using positive exponents only. $$ x^{2 / 5}\left(x^{2}-2 x^{3}\right) $$

Simplify the expression, writing your answer using positive exponents only. $$ \frac{3^{0} \cdot 4 x^{-2}}{16 \cdot\left(x^{2}\right)^{3}} $$

Solve the given equation. $$ \sqrt{k+1}+\sqrt{k}=3 \sqrt{k} $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 8 m^{3}+1 $$

Perform the indicated operations and simplify. $$ (2 x-y)\left(3 x^{2}+2 y\right) $$

Perform the indicated operations and simplify. \(\frac{a x+b y}{a x-b x}+\frac{a y-b x}{b y-a y}\)

Evaluate the expression. $$ |2 \sqrt{3}-3|-|\sqrt{3}-4| $$

Solve the equation by using the quadratic formula. $$ m^{4}-13 m^{2}+36=0 $$

Carry out the indicated operation and write your answer using positive exponents only. $$ s^{1 / 3}\left(2 s-s^{1 / 4}\right) $$

Simplify the expression, writing your answer using positive exponents only. $$ \frac{5 x^{2}\left(3 x^{-2}\right)}{\left(4 x^{-1}\right)\left(x^{3}\right)^{-2}} $$

Solve the given equation. $$ \sqrt{x+1}-\sqrt{x}=\sqrt{4 x-3} $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 27 m^{3}-8 $$

Indicate whether the statement is true or false. $$ \text { If } a b=0 \text { and } a \neq 0 \text { , then } b=0 \text { . } $$

Perform the indicated operations and simplify. $$ \left(3 m-2 n^{2}\right)\left(2 m^{2}+3 n\right) $$

Perform the indicated operations and simplify. \(\frac{1+\frac{1}{x}}{1-\frac{1}{x}}\)

Solve the equation by using the quadratic formula. $$ y^{4}-5 y^{2}+6=0 $$

Carry out the indicated operation and write your answer using positive exponents only. $$ 2 p^{3 / 2}\left(2 p^{1 / 2}-p^{-1 / 2}\right) $$

Simplify the expression, writing your answer using positive exponents only. $$ \frac{2^{2} u^{-2}\left(v^{-1}\right)^{3}}{3^{2}\left(u^{-3} v\right)^{2}} $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 8 r^{3}-27 s^{3} $$

Perform the indicated operations and simplify. $$ (2 x+3 y)^{2} $$

Perform the indicated operations and simplify. \(\frac{2+\frac{2}{x}}{x-\frac{2}{x}}\)

Suppose \(\boldsymbol{a}\) and \(\boldsymbol{b}\) are real numbers other than 0 and \(a>b\). State whether the inequality is true or false. $$ \frac{a}{b}>1 $$

Solve the equation by using the quadratic formula. $$ 4 x^{4}-21 x^{2}+5=0 $$

Carry out the indicated operation and write your answer using positive exponents only. $$ 3 y^{1 / 3}\left(y^{2 / 3}-1\right)^{2} $$

Simplify the expression, writing your answer using positive exponents only. $$ \frac{\left(3 a^{-1} b^{2}\right)^{-2}}{\left(2 a^{2} b^{-1}\right)^{-3}} $$

Solve the equation for the indicated variable. $$ a x+b y+c=0 ; y $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ x^{3}+64 y^{3} $$

Perform the indicated operations and simplify. $$ (3 m-2 n)^{2} $$

Perform the indicated operations and simplify. \(\frac{\frac{1}{x}+\frac{1}{y}}{1-\frac{1}{x y}}\)

Suppose \(\boldsymbol{a}\) and \(\boldsymbol{b}\) are real numbers other than 0 and \(a>b\). State whether the inequality is true or false. $$ a^{2}>b^{2} $$

Solve the equation by using the quadratic formula. $$ 6(x+2)^{2}+7(x+2)-3=0 $$

Write the expression in simplest radical form. $$ \sqrt{32} $$

Simplify the expression, writing your answer using positive exponents only. $$ (-2 x)^{-2}(3 y)^{-3}(4 z)^{-2} $$

Solve the equation for the indicated variable. $$ p=-3 q+1 ; q $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ u^{2} v^{6}-8 u^{2} $$

Indicate whether the statement is true or false. $$ (a-b)-c=a-(b-c) $$

Perform the indicated operations and simplify. $$ (2 u-v)(2 u+v) $$