Problem 78 - Algebra 1

Question

Simplify the variable expression. $$(-6)(y)$$

Step-by-Step Solution

Answer

-6y

Step 1: Identify the operation and operands

The operation presented in the exercise is multiplication. The operands are -6 and variable y.

Step 2: Multiply the constant with the variable

Multiplying -6 with y gives -6y. In algebra, when a constant is multiplied with a variable, the operation is implied and usually denoted this way.

Key Concepts

Understanding Simplification in Algebra

Simplification is an essential technique in algebra. It involves rewriting expressions in the simplest form for easier understanding or solving. Think of it like cleaning a messy room and organizing everything neater. When simplifying algebraic expressions, the goal is to make the equation as straightforward as possible without changing its value.

• Identify operations like addition, subtraction, multiplication, and division.
• Combine like terms, such as grouping similar variables or constants.
• Apply the order of operations correctly (remember PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).

In the exercise, simplifying meant performing the multiplication of a constant and a variable. The result, \(-6y\), is simpler because it combines the operations into one clear expression.

Effective Approach to Multiplying Constants

Multiplying constants involves straightforward arithmetic, but it's essential to execute it correctly, especially within algebraic expressions. A constant is simply a number without a variable attached, such as -6 in this scenario.

• When a constant is multiplied with a variable, like \(y\), the result combines them into a single term.
• If you multiply negative and positive numbers, remember a negative times a positive stays negative.

Using the given operation \((-6)(y)\), apply multiplication, and it results in \(-6y\). This step is fundamental in algebra as it helps reduce the complexity of expressions, making them manageable and less prone to errors in further calculations.

The Role of Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and operations. They form the foundation of algebra, allowing us to generalize and solve a variety of mathematical problems.

• Expressions can include operations like addition, subtraction, multiplication, and division.
• Variables represent unknown values and can take different forms.
• Constants are fixed values that anchor the expression.

In our example, \(-6y\) is classified as an algebraic expression. Here, \(-6\) is a constant, and \(y\) is a variable, collectively illustrating how these components interact. Such expressions give us the flexibility to solve equations by substituting or manipulating their terms.