This week’s discussion asks that we evaluate algebraic expressions.
In this initial post I will be referring to the following words to demonstrate my understanding of their meaning and how it relates to my work.
Exponent, Integer, Variable, Lowest terms, and Divisor.

I used my son’s birthdate for the first part of this assignment and it is December 7, 1993. This means that I will be using the following integers to solve the following three expressions. a = 12, b = -17, and c = 93

I will be using algebraic expressions in problems A-C given in this week’s assignment.

A. a3 – b3 This is the given expressions with variables a and b exponents of 3 on each of them. 123 – (-173) I have plugged in 12 for variable a and -17 for variable b. 1728 – (-4913) The integers were raised to the given exponents. 1728 + 4913 When you minus a negative it becomes a plus. 6641 Here is my final answer.

B. (a – b)(a2 + ab + b2) This given expression uses variables a and b. [12 – (-17)][122 + 12(-17) + (-17)2] I have plugged in 12 for a and -17 for b in each problem. [12 + 17][144 + (-204) + 289] In the first part the two negatives became a plus, and in The second part the squaring and the multiplication was done. 29(144 – 204 + 289) The first addition was done and the signs were simplified. 29(229) The second quantity was simplified. 6641 Here is my answer.

C. (b – c) _ This last expression uses all three variables: a, b, and c. (2b – a) It is a rational expression with a divisor of 2b – a. -17 – 93_ The integers have been plugged in for the variables. 2(-17) – 12 - 110_ Both numerator and denominator have been evaluated. - 46 Both are negative which means the answer will be positive. _55_ This is my answer in lowest terms, and I will leave the 23 answer as an improper fraction.

In conclusion I did notice that my answers are the same for problems A and B.