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Chapter 2: Problem 58

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$(-y)^{2}$$

Short Answer

Expert verified
(3)^{2} = 9.

Step by step solution

01

Understand the expression

Identify the given variables and the expression to be evaluated. The expression is overseer (-y)^{2}, and the given values are x=2, y=-3, and z=-4.We need to evaluate the expression overseer (-y)^{2} using y=-3..
02

Substitute the value of y

Replace the variable y in the expression with the given value y=-3.The expression becomes overseer (-(-3))^{2}.
03

Simplify the expression

Simplify the expression inside the parentheses first. Since (-(-3)) equals 3, the expression is (3)^{2}.
04

Calculate the square

Finally, calculate the square of 3. (3)^{2}=9.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Substitution
Substitution is the process of replacing the variables in an expression with the given values. This step is crucial for evaluating expressions accurately. In our exercise, we started with the expression `(-y)^{2}` and were given the values `x=2`, `y=-3`, and `z=-4`. To evaluate the expression, we only needed the value of `y`.

Here's what we did:
  • Identify the variable in the expression: `y`.
  • Replace `y` with `-3`, as provided: `(-(-3))^{2}`.
By carefully substituting the values, you ensure that all variables are correctly accounted for. This step is fundamental in algebra and helps set the stage for further simplification and solving.
Simplification
Simplification involves reducing the expression to a simpler form. Once variables are substituted, you need to simplify the mathematical operations involved.

For our specific problem:
  • After substituting the given value, the expression became `(-(-3))^{2}`.
  • The negative signs within the parentheses needed to be simplified: `-(-3)` is equivalent to `3`.
Now, the expression is much simpler: `3^{2}`. Keep track of your steps and deal with one operation at a time, which makes the problem more manageable and less prone to errors.
Squaring Numbers
Squaring is a mathematical operation where a number is multiplied by itself. It is represented with an exponent of 2: `n^{2}` means `n*n`. Understanding squaring is crucial for evaluating expressions involving squares.

Here's how we handle squaring:
  • After simplification, our expression became `3^{2}`.
  • Calculate the square by multiplying 3 by itself: `3 * 3 = 9`.
Thus, `3^{2} = 9`. Squaring is a fundamental operation in many areas of math and appears regularly in algebra, geometry, and calculus. Ensuring accuracy in squaring will help in doing more complex calculations down the line.

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