The following 25 problems are worth 0.2 extra credit point each, for a total of up to 5 points. Submit to the Extra Credit Drop Box.

1. Watch the videos Combining Like Terms & The Distributive Property and Adding and Subtracting Polynomials Then do the following:

A) Add (3x2 + 2x + 1) + (4x2 + 3). Remember to only combine LIKE terms. ANSWER: 7x2 + 2x + 4

B) Subtract (12x3 + 3x2 - 5) - (10x3 - 5x2 + 1). ANSWER: 2x3 + 8x2 - 6

C) Use the Distributive Property to multiply out 2(x + 3). ANSWER:2x +6

D) Use the Distrbutive Property twice in 3(x + 4) + 5(x + 2) and then combine like terms. Your answer will consist of an x-term and a numerical term. ANSWER: 8x + 22

E) Use the Distrbutive Property twice in 3(x + 4) - 2(x + 2) and then combine like terms. Your answer will consist of an x-term and a numerical term. Note that this the same problem as 3(x + 4) + (-2)(x + 2) where you multiply -2 times each of the two terms of x+2. ANSWER: x + 8

2. Watch the video Exponent Rules Then do the following:

A) Multiply x3 • x4 and write as a single power of x. ANSWER: x7

B) Multiply (x5)3 and write as a single power of x. Note: This is the same as x5 • x5 • x5. ANSWER: x15

C) Divide x7/x2 and write as a single power of x. ANSWER: x5

D) Multiple (2x3)4. Note that this is the same as 2x3 • 2x3 • 2x3 • 2x3. ANSWER: 16x12

E) Write x-3 as a fraction with a positive power on x. ANSWER: 1/x3

F) What does (2x)0 simplify to? ANSWER: 1

G) What does 1/(2x)-2 simplify to? Note that this is 1 over the quantity of (2x) raised to the negative 1 power. ANSWER: 4x2

3) Watch the video Multiplying Terms With Exponents. Then do the following:

A) Multiply (2x3) • (3x2) ANSWER: 6x5 B) Multiply (3x4) • (-2x3) ANSWER: -6x7

C) Multiply (2xy2) • (2xy)2 , a problem very similar to one shown in the video at the 4:26 place in the video. ANSWER: 8x3y4

4) Watch the video Multiplying a Term Times a Polynomial and then do the following:

A) Multiply 5a(4a2 + 3a) and simplify. (Very similar to first problem of video) ANSWER: 20a3 + 15a2

B) Multiply 3x2(5x3 - 2x). Remember that after you mulitply you can not combine these unlike terms! ANSWER: 15x5 – 6x3

C) Multiply x3(x2 - 3x + 3). ANSWER: x5 - 3x4 + 3x3

5) Apply both the principles of the Distributive Property, Exponent Properties, and Combining Like Terms, to multiply out the following and simplify. Remember that ONLY like terms may be combined!

A) 4x(x + 1) + 3x(x + 5) ANSWER: 7x2 + 19

B) 3x(x + 5) - 2x(x + 4) ANSWER: x2 + 7x

C) 3x2(x2 + 3x) + 2x(x3 + x) ANSWER: 6x4 + 9x3 + 2x2

D) 2x(x2 + 5x + 3) + 4x2(x + 3) ANSWER: 6x3 + 22x2 + 6x

6) Watch the video The FOIL Method and do the following:

A) Multiply (x + 3)(x + 2) and combine like terms. Your answer should have 3 terms! ANSWER: x2 + 5x + 6

B) Multiply (3x - 3)(2x - 5) and combine like terms. ANSWER: 6x2 -21x + 15

C) Muliply (4x + 2)(4x - 2) and combine like terms. ANSWER: 16x2 - 4