This is an algebra review. See me in office hours or during an appointment to discuss their answers. Warning: printing this page may produce some funny symbols.

1. We need to be able to cancel common terms. Simplify the following (if you can)

   1. $$\frac{a + ab + a^b}{a^2}$$

   2. $$\frac{a + h + 2a}{h}$$

   3. $$\frac{a^2 - 4}{a + 2}$$

2. Let’s make sure we can expand polynomials: Expand the following using a formula or the FOIL method.

   1. $(x+2)^2$

   2. $(a - b)^3$

3. What about factoring? Factor the following polynomials.

   1. $x^2 - 3x -10$

   2. $-16x^2 + 16 x +32$

   3. $x^2 - 16$

4. Simplify if you can

   1. $$\frac{x^2 - 3x - 10}{x^2 - 4}$$

   2. $$\frac{x^2 + 9}{x^2 - 9}$$

5. Combining fractions is really important. Try your hand at these. Write the following as a combined fraction. Simplify as much as possible,

   1. $$\frac{1}{x+2} - \frac{1}{x-2}$$

   2. $$\frac{\frac{1}{x+h} - \frac{1}{x}}{h}$$

   3. $$\frac{1}{x^2} + \frac{1}{x + 3}$$

6. Knowing how to deal with powers is also important. Simplify the following.

   1. $(a^3 b^2 c^1)^4$

   2. $a^{(1/4)} a^{4}$

   3. $(a^{1/2} a^2)^3$