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Chapter 2: Problem 87

Evaluate the expressions for the given values of the variables. $$x^{2} \text { for } x=-3$$

Short Answer

Expert verified
The value is 9.

Step by step solution

01

- Identify the given variable

The expression to evaluate is \(x^{2}\), and the given value for the variable is \(x = -3\).
02

- Substitute the variable into the expression

Substitute \(x = -3\) into the expression \(x^{2}\). This yields \((-3)^{2}\).
03

- Compute the value of the expression

Calculate \((-3)^{2}\). Since squaring a number means multiplying it by itself, perform the multiplication: \((-3) \times (-3) = 9\).

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Key Concepts

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

prealgebra
Prealgebra is the foundation for all higher-level math courses. It's where you learn basic operations and concepts that you will use as building blocks for more complex topics.
Prealgebra involves:
  • Addition, subtraction, multiplication, and division
  • Basic properties of numbers (associative, commutative)
  • Understanding and manipulating variables
In many problems, you will have to evaluate expressions by substituting values into variables.
Let's dive deeper into substitution, which will help you tackle such problems effortlessly.
substitution
Substitution is a method used to replace a variable with its given value. This process simplifies expressions and allows you to solve them.
Steps for substitution include:
  • Identify the variable and its value
  • Replace the variable with its given value in the expression
  • Simplify the expression as needed
For example, in the given problem, we need to evaluate the expression \(x^{2}\) for \(x=-3\).
By substituting \(x=-3\) into the expression, we get \((-3)^{2}\).
With substitution done, let鈥檚 move on to the next crucial concept: squaring numbers.
squaring numbers
Squaring a number means multiplying the number by itself.
The notation for squaring a number is \(n^{2}\), where \(n\) is the number.
So, if you square \(4\), it looks like this: \(4^{2} = 4 \times 4 = 16\).
For the problem we are solving:
We substitute \(x\) with \(-3\) to get \((-3)^{2} = -3 \times -3\).
Keep in mind, squaring any number, whether positive or negative, results in a positive number.
So, \((-3)^{2} = 9\).
This leads us to another important aspect when dealing with negative numbers.
negative numbers
Negative numbers are less than zero and can be tricky to handle in calculations.
When you multiply two negative numbers, the result is positive:
  • \((-a) \times (-b) = ab\)
For example, in our problem, \((-3) \times (-3) = 9\).
It's important to remember that negative signs cancel each other out when multiplied.
Understanding this can help prevent mistakes in your calculations.
Additionally, keep this rule in mind: adding and subtracting negative numbers follows different rules than multiplying them.
Negative numbers are crucial in prealgebra and further math, so practice them well!

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