MAT221 Discussions Week 1: Evaluating Algebraic Expressions

Evaluating Algebraic Expressions
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Evaluating Algebraic Expressions
Birth date: January 6, 1983, written as 1/12/1967
Now, a = one-digit month number = 1
b = the negative one-digit day number = -12
c = the tow-digit year number = 67.
Now, let us evaluate the values of the given expressions by substituting the three variables in the expressions, of a, b, and c using their respective values given above. The three expressions are given below:
* a3 – b3
* (a – b) (a2 + ab + b2)
* (b-c)2b-a
* Substituting the for the three variables in a3 – b3 yields,
13 – (-12)3= 1- (-1728) (Note that the value of (-12)3 is a negative integer because it is raised by the power of an odd exponent).
Thus, 1- (-1728) = 1 + 1728 = 1729 (note that a negative followed by another negative becomes a positive)
Substituting the variables in the second expression yields;
(a – b) (a2 + ab + b2) = (1- -12) (12 + 1×-12 + -122)
= (1+12) (1-12+144)
13× 133 = 1729
Substitution the variables in the third expressions with their respective values yields,
(b-c)(2b-a) = (-12-67)(2×-12-1)
= -79-25
In the above improper fraction, there is a negative sign on both the denominator and the numerator and thus it cancels out. In addition...