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Chapter 2: Problem 48

Evaluate each expression. \(-2 x y,\) if \(x=-8\) and \(y=5\)

Short Answer

Expert verified
The value of the expression is 80.

Step by step solution

01

Substitute the Given Values

The exercise asks us to evaluate the expression \(-2xy\) using the values \(x = -8\) and \(y = 5\). The first step is to substitute these values into the expression. This gives us: \(-2(-8)(5)\).
02

Simplify the Expression

Next, we need to perform the multiplication. Start by multiplying \(-2\) and \(-8\), which results in \(16\) because multiplying two negative numbers results in a positive number. Now, multiply \(16\) by \(5\) to get \(80\).
03

Confirm the Solution

After performing the calculations, our outcome for the expression \(-2xy\) with the given values is \(80\). Double-check all arithmetic operations to ensure the calculations were performed correctly.

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Key Concepts

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

Substitution in Algebra
Substitution in algebra is a fundamental concept that simplifies evaluating expressions by replacing variables with their given values. When you encounter an algebraic expression like
  • \(-2xy\),
the first step is to substitute the provided values for each variable. In our example:
  • \(x = -8\)
  • \(y = 5\)
We rewrite the expression by directly replacing \(x\) and \(y\) with these numbers, transforming \(-2xy\) into
  • \(-2(-8)(5)\).
This operation prepares the expression for evaluation, setting the stage for the next steps in solving the problem. Remember, accurate substitution is essential to ensure correct results when simplifying expressions.
Expression Evaluation
Expression evaluation involves performing arithmetic operations to find the numerical value of an algebraic expression. Once substitution is done,
  • like in our example: \(-2(-8)(5)\),
we move on to evaluate this expression by following the rules of arithmetic. It generally means carrying out operations in the correct sequence such as multiplication, division, addition, and subtraction.

In this case, the expression is composed only of multiplication, so we simply execute the operations from left to right. Following the correct order ensures a clear and accurate path to the final numerical result, which helps in avoiding errors.
Multiplication of Integers
Multiplying integers, especially dealing with negative signs, requires an understanding of how these numbers interact.
  • When two integers are multiplied, the sign of the result depends on the signs of the integers being multiplied.
  • Two negatives make a positive, so multiplying any two negative numbers yields a positive product.
  • Conversely, a negative times a positive results in a negative product.
For our expression
  • \(-2(-8)(5)\),
we start by multiplying the two negative numbers: \(-2\) and \(-8\). This gives us a positive \(16\), as the two negatives cancel each other's effect. Next, multiply \(16\) by \(5\) to get \(80\).

Practicing these rules repeatedly enhances your fluency with multiplications involving integers, giving you a solid base for tackling complex algebraic expressions.

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