Evaluating Algebraic Expressions: Read The Instructions Belo

Evaluating Algebraic Expressions Read The Instructions Below To Comp

Evaluate algebraic expressions based on a given birth date in mm/dd/yy format, define variables a, b, and c from this date, and substitute these into provided algebraic expressions. Use the specified instructions to compute the expressions and incorporate five math vocabulary words—exponent, integer, variable, lowest terms, and divisor—into your discussion.

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To illustrate the process of evaluating algebraic expressions in relation to personal data, I will use my own birth date, which is August 15, 1990, written as 8/15/90. Accordingly, the variables are assigned as follows: a = 8 (the month), b = -15 (the negative of the day), and c = 90 (the year). These variables serve as the foundation for plugging into the algebraic expressions provided in the assignment.

First, consider the expression a3 – b3. Using the assigned variables, this becomes 83 – (-15)3. Calculating these, 83 equals 512, and (-15)3 equals -3375 because cube of a negative integer remains negative. Thus, a3 – b3 equals 512 – (-3375). Since subtracting a negative is equivalent to addition, the expression simplifies to 512 + 3375, resulting in a total of 3887. This demonstrates how the exponent affects calculation, raising each variable to the third power, which is a form of applying the exponential function.

Next, evaluate the expression (a – b)(a2 + ab + b2). Substituting in the values, it becomes (8 – (-15))(82 + 8)(-15) + (-15)2). Simplifying step-by-step, the first part inside the parentheses: 8 + 15, which sums to 23. For the second part, calculate each term: 82 = 64; 8 * -15 = -120; and (-15)2 = 225. Summing these: 64 – 120 + 225 results in 169, considering the negative and positive integers involved. Then multiply 23 and 169 to reach 3887. This process underscores the importance of the variable representation and how the order of operations helps arrive at the final result, which can be expressed in the simplest form—often called lowest terms when dealing with fractions or ratios.

Finally, evaluate the simple algebraic expression b – c, substituting the assigned variables: -15 – 90, resulting in -105. This value is already in lowest terms, which confirms no further simplification is necessary. The divisor concept is demonstrated when dividing expressions or numbers, especially when reducing expressions to their simplest form or evaluating fractions.

In conclusion, evaluating algebraic expressions involving personal data like a birth date provides a practical understanding of key mathematical concepts. The exponent function applies when raising variables to powers, the integer nature of the data helps understand signs and magnitudes, and the use of variables allows flexible substitution. Simplifying expressions to their lowest terms ensures clarity and efficiency in communication, while the concept of a divisor aids in factoring and reducing expressions. These fundamental mathematical ideas underpin much of algebra and higher mathematics.

References

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