Evaluating Algebraic Expressions Write your birth date or the birth date of some

Question

  Evaluating Algebraic Expressions

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).           MY BIRTHDAY IS 5/24/76

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)

Use the following algebraic expressions for parts 3-5 of the discussion:

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.

After you have your math worked out on scratch paper, go back and verbally describe the steps you took to evaluate the expressions. Make sure to use each of the vocabulary words at least once in your writing.

Incorporate the following five math vocabulary words 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 work.):

Exponent

Integer

Variable

Lowest terms

Divisor

Your initial post should be 150-250 words in length. Respond to at least two of your classmates’ posts by Day 7. Do you agree with how your classmates used the vocabulary? Did the student handle the negatives in the formulas accurately?

  Evaluating Algebraic Expressions

Explanation / Answer

DOB: 2/8/86

Now, let a =2, b = -8 and c = 86.

Then a3-b3=23–(-8)3=8-(-512)=8+512=520; and (a-b)(a2+ab+b2)=[2-(-8)][22+2(-8)+(-8)2]=(2+8)(4-16+64)= 10(52) = 520. Thus a3-b3=(a-b)(a2+ab+b2).

Also,(b-c)/(2b-a) = (-8-86) /[2(-8)-86] = -92/(-16-86)= -92/(-102) = -41/(-51)= 41/51.

The expressions a3-b3 is equal to (a-b)(a2+ab+b2). This is no coincidence. This is true for arbitrary variables (integers or, non-integer numbers) a and b. In the expression, a3-b3, the exponent of each of a and b is 3. Further, in the expression (b-c)/(2b-a), the number 2b-a is the divisor. Also, (b-c)/(2b-a) is equal to the fraction -92/(-102) which can be further simplified to 41/51, its lowest term.

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