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Evaluating Algebraic Expressions
1. Write your birth date or the birth date of someone in your family as mm/dd/yy. (Example :
March 13, 1981 is written 3/13/81, and November 7, 1967 is written 11/7/67).
•
•
•
Now let a = the one- or two- digit month number,
B= the negative of the one- or two- digit day number, and
C= the two- digit year number.
( Our example: a=3, b= - 13, and c= 81 or a= 11, b= -7, and c=67)
2. Use the following alegebraic expressions for parts 3-5 of the discussion:
• A3- b3
• (a-b) (a2+ a b + b2)
• (b- c)
(2 b – a)
3. Evaluate the three given expressions using the a, b, and c from your birth date. Make sure that b
is negative when you plug in the values.
4. After you have your math worked out on scratch paper, post your results as well as a description
of the steps you took to evaluate the expressions.
•
Did you notice anything interesting about the results of a3 - b3 and (a-b) (a2 + abt b2 ) ?
was this coincidence or do you think there is a reason for this?
Incorporate the following five math vocabulary words at least once into your discussion. Use bold font
to emphasize the words in your writing ( Do not write definitions for the words; use them appropriately
in sentences describing your math works.)
o
o
o
o
o
Exponent
Integer
Variable
Lowest terms
Divisor
0nly have 150- 250 words in explaining things and no plagiarism please. Follow directions and
add reference.

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.]

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