Question

Difficulty: HardOrder of Operations and Number Properties

An algebra student is simplifying the expression $a(b - c) - d(e - f)$ by applying the distributive property. Instead of distributing correctly, the student incorrectly writes the expansion as $a(b - c) - de - df$ . If $a = 2$ , $b = 3$ , $c = 5$ , $d = -3$ , $e = 4$ , and $f = -2$ , what is the absolute difference between the student's incorrect result and the correct value of the expression?

Answer: 12

Answer

The correct answer is 12.

The correct expression evaluates to 14, and the incorrect expression evaluates to 2. The absolute difference between them is

|14 - 2| = 12

.

Step-by-Step Solution

1

Evaluate the correct expression

a(b - c) - d(e - f)

using the given values.

14

To find the mathematically correct value of the expression.

2

Evaluate the incorrect expression

a(b - c) - de - df

using the same values.

2

To find the value resulting from the student's distribution error.

3

Find the absolute difference between the correct value and the incorrect value.

12

To determine the error magnitude as requested by the question.

Key Concept

Distributive Property and Order of Operations

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Topics

Order of Operations and Number Properties

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