Problem 89 - Algebra 1

Question

Evaluate the expression. \(-4 x y\) when \(x=-2\) and \(y=-6\)

Step-by-Step Solution

Answer

The evaluated expression is -48.

Step 1: Substitute the given values

Replace \(x\) with -2 and \(y\) with -6 in the original expression. This gives us: \(-4*(-2)*-6\).

Step 2: Apply order of operations

When dealing with multiple operations in the same expression, we apply the rules of order of operations, also known as BIDMAS or PEMDAS. However, in this case, there is only multiplication. So we proceed from left to right. This results in: \(8*-6 = -48\).

Key Concepts

Order of Operations

When solving any mathematical expression, it’s crucial to follow the **order of operations** to obtain the correct answer. This set of rules ensures consistent results and clarity when multiple operations exist in a single expression. Generally abbreviated as BIDMAS or PEMDAS, this rule sequence stands for:

• **B**rackets/Parentheses
• **I**ndices/Exponents
• **D**ivision
• **M**ultiplication
• **A**ddition
• **S**ubtraction

In the exercise provided, we only perform multiplication, which means we can solve it from left to right without any additional steps. When more complex expressions are involved, always remember to tackle them in the order of BIDMAS/PEMDAS. This ensures that each part of the expression is correctly and logically solved.

Substitution

The concept of substitution helps simplify expressions by replacing variables with their given numerical values. This process is vital when evaluating expressions, making them easier to work with. In this exercise, we're given specific values for our variables:

• **Substitute** \( x = -2 \)
• **Substitute** \( y = -6 \)

By inserting these values into the expression \( -4xy \), we transform it into a purely numeric expression: \(-4 \times (-2) \times (-6)\).
Substitution allows you to convert algebraic expressions into basic arithmetic problems, paving the way for straightforward calculation and evaluation.

Algebraic Expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operation symbols. They are crucial for solving real-world problems and represent relationships between different variables. In this exercise, the expression \( -4xy \) represents a product involving the variable terms \( x \) and \( y \), along with the constant \(-4\).
Such expressions become useful when you need to compute values given specific variable assignments. They can be manipulated through algebraic rules and operations to simplify or rearrange them for different applications.

• Understanding how to work with algebraic expressions helps in recognizing patterns and solving problems effectively.
• They form the backbone of many real-life calculations, from finance to engineering applications.

Grasping the concept of algebraic expressions can significantly enhance your mathematical problem-solving abilities.