Question 1

Evaluate the expression if $$x = -2$$, $$y = -4$$, and $$z = 1$$:

$$\dfrac{\left|2y\right| - \left|x\right|^2}{\left(y - 3z\$$right)^2$$}$$

Accepted Answer

$$\dfrac{8 - 4}{49} = \dfrac{4}{49}$$

Question 2

Evaluate the expression if $$x = 1$$, $$y = -2$$, and $$z = 3$$:

$$\dfrac{-4\left|2x + 3y\right|}{2y^2$ - z}$$

Accepted Answer

$$\dfrac{-4\left|2 + (-6)\right|}{2 \cdot 4 - 3} = \dfrac{-4\cdot 4}{5} = -\dfrac{16}{5}$$

Question 3

Evaluate the expression if $$x = -2$$, $$y = -1$$, and $$z = 3$$:

$$\dfrac{-x^2$ + 3\left|y\right|}{x\left(y + 2z\right)}$$

Accepted Answer

$$\dfrac{-4 + 3\cdot 1}{-2(-1 + 6)} = \dfrac{-4 + 3}{-2\cdot 5} = \dfrac{-1}{-10} = \dfrac{1}{10}$$

Question 4

Simplify the following expression:

$$\dfrac{3a + 4b}{7a - 5b} - \dfrac{4a - 9b}{5b - 7a}$$

Accepted Answer

$$\dfrac{3a + 4b + 4a - 9b}{7a - 5b}$$

Question 5

Simplify the following:

$$\dfrac{xy}{\dfrac{11}{x} + \dfrac{11}{y}}$$

Accepted Answer

$$\dfrac{xy}{\dfrac{11(x + y)}{xy}} = \dfrac{x^2$y^2$$}{11(x + y)}$

Question 6

Expand and simplify:

$$\$$left(x^2$$ + 2y\right)\$$left(x^2$$ - 2y\right)$$

Accepted Answer

$$x^4$$ - $$4y^2$$

Question 7

Simplify:

$$x(x^2 - 1$$) - $$x^2(x + 2) - x(2x - 2$$)$$

Accepted Answer

$$-2x^2 + 2x$

Question 8

Multiply and simplify:

$$\dfrac{3x^2$ + 7x + 2}{x^2$ + 2x} \cdot \dfrac{x^2$ - x}{3x^2$ + x}$$

Accepted Answer

$$\dfrac{(3x + 1)(x + 2)(x)(x - 1)}{x(x + 2)(3x + 1)x}$$

Question 9

Simplify:

$$\dfrac{2x}{x^2$ - 25} - \dfrac{x + 1}{x^2$ + 5x}$$

Accepted Answer

$$\dfrac{x - 1}{x^2$ - 25}$$

Question 10

Factor completely:

$$x^3y^2$ - 4x^3$ + 8y^2$ - 32$

Accepted Answer

$$(x^3$$ + $$8)(y^2 - 4$$)$$

Question 11

Factor completely:

$$8a^3$$ + $$64b^3$$

Accepted Answer

$$8(a + 2b)(a^2$ - 2ab + 4b^2$)$$

Question 12

Simplify and write with no negative exponents:

$$\left(\dfrac{x$$^{2/3}$$y^{3/4}z$$^{-1/2}$$}{x$$^{-1/4}$$z^{-1/6}$$}\$$right)^{-6}$

Accepted Answer

$$x^{5/12}y$$^{9/8}$$z^{2/3}$$

Question 13

Simplify and write with no negative exponents:

$$\left(\dfrac{a$$^{2/3}$$b^{-3/4}c$$^{-1/5}$$}{a$$^{1/2}$$b^{1/4}$$}\$$right)^{10}$

Accepted Answer

$$a^{5/3}b$$^{-10/2}$$c^{-2}$$

Question 14

Simplify:

$$\sqrt{75x$$^{16}$$y^7z$$^{10}$$}$$

Accepted Answer

$$5x^8y^3$z^5$$\sqrt{3y}$$

Question 15

Rationalize the denominator and simplify:

$$\dfrac{12}{5 - 2\sqrt{7}}$$

Accepted Answer

$$\dfrac{12(5 + 2\sqrt{7})}{(5 - 2\sqrt{7})(5 + 2\sqrt{7})} = \dfrac{60 + 24\sqrt{7}}{25 - 28} = \dfrac{60 + 24\sqrt{7}}{-3}$$

College Algebra Exam Review: Evaluating Expressions and Simplifying Algebraic Forms

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