Problem 86 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. (Lesson 2.5) $$-5(-n)(-n) \text { when } n=2$$

Step-by-Step Solution

Answer

-20

Step 1: Substitute Variable

The first step will be to substitute the given value of \( n \) into the expression. This will result in the expression becoming -5(-2)(-2).

Step 2: Multiply Numbers

The next step is to apply the multiplication. Taking into account the rules for multiplication, and particularly the rule which states that the product of two negative numbers is a positive number, gives -5 * 4.

Step 3: Final Calculation

In the last step, the multiplication of -5 and 4 has to be calculated. This results in a value of -20

Key Concepts

Substitution

Substituting involves replacing a variable with a given number or value. In the exercise, you are told to evaluate an expression when the variable \( n \) equals 2.

• Identify the variable: In this example, it is \( n \).
• Replace the variable: Change all occurrences of \( n \) in the expression to the number 2, transforming \( -5(-n)(-n) \) into \( -5(-2)(-2) \).
• Re-examine the expression: Ensure all substitutions are correct before moving to the next step.

Substitution is the first crucial phase in evaluating algebraic expressions because it sets up the equation for calculation with actual numbers.

Multiplication of Integers

Multiplication of integers involves some straightforward but important rules. When you're dealing with multiple integers, especially negatives, it's crucial to apply these rules correctly.
1. **Product of Two Negatives**: Multiplying two negative numbers always results in a positive number. Thus, \((-2)\times(-2)\) becomes \(4\).2. **Next Multiplication Step**: Continue with multiplying this result by the integer outside the parentheses. Multiply \(-5\) by \(4\), which results in \(-20\).
These steps illustrate how properly handling negative signs influences the outcome of multiplication in algebraic expressions.

Negative Numbers

Negative numbers often confuse students, but once you grasp the basic rules, they are straightforward to handle.

• **Negative Signs in Substitution**: Be mindful of the negative signs when performing substitution. Changes in signs can shift the final answer significantly.
• **Multiplying Negatives**: Remember that the product of two negative numbers is positive, but multiplying a positive by a negative results in a negative product.
• **Expression Outcome**: For the expression \(-5\times4\), recall that a single negative times a positive yields a negative result, leading to \(-20\).

Understanding negative numbers and their impact in multiplication ensures you evaluate algebraic expressions accurately every time.