INSTRUCTOR GUIDANCE EXAMPLE: Week One Discussion 1. I will use the following five vocabulary words in my discussion demonstrating my understanding of their meaning as relating to the math work. exponent integer variable lowest terms divisor 2. I will be using my sister's birth date for this exercise, and it is 21 October 1961. This means I have the following integers to work with: Let a = 10 b = -21 (notice I made the day number negative) c = 61 I will be using the algebraic expressions in A - C given in the assignment for parts 3 - 5 of the discussion. A) a3 - b3 This is the given expression with variables a and b and exponents of 3 on each of them 103 - (-21)3 I have plugged in 10 for variable a and -21 for variable b. 1000 - (-9261) The integers were raised to the given exponents. 1000 + 9261 Minus a negative becomes a plus. 10,261 Here is the final answer. B) (a - b)(a2 + ab + b2) This is the given express which also uses variables a and b. [10 - (-21)][102 + 10(-21) + (-21)2] I have plugged in 10 for a and -21 for b in each case. [10 + 21][100 + (-210) + 441] In the first part the two negatives became a plus, and in the second part the squaring and the multiplication was done. 31(100 - 210 + 441) The first addition was done and the signs were simplified. 31(331) The second quantity was simplified. 10,261 Here is the final answer. C) b-c 2b - a - 21 - 61 2(-21) - 10 - 82 - 52 41 26 This expression uses all three variables: a, b, and c. It is a rational expression with a divisor of 2b - a. The integers have been plugged in for the variables. Both numerator and denominator have been evaluated. Both are negative which means the answer will be positive. This is our answer in lowest terms, and I will leave the answer as an improper fraction. 6. [Student answers will vary on this question depending upon math background and memory.]