Problem 40 - Algebra 1

Question

List the terms of the expression. $$(-n)(-n)(-4)$$

Step-by-Step Solution

Answer

The term in the expression \(-n)(-n)(-4\) is \(-4n^2\).

Step 1: Identify Numbers and Variables

Identify the numbers and variables in the expression, in this case, we have three terms, two of which are \(-n\) and one \(-4\).

Step 2: Apply Multiplication Rule

Apply the multiplication rule for negative numbers. Multiplying two negative numbers yields a positive number. Thus \((-n)(-n)\) would give \(n^2\).

Step 3: Further Multiplication

Multiply the result of \(-n) times \(-n) with the remaining \(-4)\. Since a positive number times a negative number equals a negative number, we have \(n^2 times -4 = -4n^2.\)

Step 4: Final Result

The final term will be \(-4n^2\). Thus, in the expression \(-n)(-n)(-4\) the only term is \(-4n^2\).

Key Concepts

Expressions

In algebra, an expression is a combination of numbers, variables, and operators (such as addition and multiplication) that represent a specific value. Unlike equations, expressions do not contain an equality sign and are instead used to describe mathematical quantities. For example, the expression \((-n)(-n)(-4)\) consists of numbers and variables multiplied together. Expressions can be simplified by following the rules of arithmetic and algebra. Simplifying expressions helps to evaluate or transform them into a more manageable form. To better understand expressions, break them down into individual components to analyze and manipulate them.

Terms of an Expression

Terms of an expression refer to the individual parts that are added or subtracted in an expression. However, when the expression involves multiplication, as in \((-n)(-n)(-4)\), we focus on the factors. Here, the expression consists of three factors: \(-n\), \(-n\), and \(-4\).
Each of these factors contributes to the expression's overall value. It's important to recognize that terms can involve both constants (like -4) and variables (like \(n\)).
They can also include combinations of both, as in \(-4n^2\). By identifying these parts, you can better manipulate and simplify expressions.

Multiplication Rules

Understanding multiplication rules is crucial to working with expressions that involve variables and numbers. One key rule is that multiplying two negative numbers results in a positive number. For the expression \((-n)(-n)(-4)\), the multiplication \((-n)\times(-n)\) gives \(n^2\) because two negatives make a positive.
Another important rule is that multiplying a positive number by a negative number results in a negative number. Thus, when you multiply \(n^2\) by \(-4\), you get \(-4n^2\). These rules help simplify expressions and accurately determine their value.