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math221_week_1_discussion_1_example.docx

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 This expression uses all three variables: 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.