Math 221 Intro to Algebra Week 1 DQ 1

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 expressio ns in A – C given in the assignment for parts 3 – 5 of the discussion. A) a3 – b3 This is the given expression with variable s a and b and exponent s of 3 on each of them 10 3 – (-21) 3 I have plugged in 10 for variable a and -21 for variable b. 1000 – (-9261) The integer s were raised to the given exponent s. 1000 + 9261 Minus a negative becomes a plus. 10,261 Here is the final answer. B) (a – b)(a 2 + ab + b 2) This is the given express which also uses variables a and b. [10 – (-21)] [10 2 + 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 This expression uses all three variable s: a, b, and c. 2b – a It is a rational expression with a divisor of 2b – a. – 21 – 61 The integers have been plugged in for the variables . 2(-21) – 10 – 82 Both numerator and denominator have been evaluated. – 52 Both are negative which means the answer will be positive. 41 This is our answer in lowest terms , and I will leave the 26 answer as an improper fraction. 6. [Student answers will vary on this question depending upon math background and memory.]