Question

complete the following sentence so that the resulting statement is true.

the expression (x^3 - 8) is called a ______.

the expression (x^3 - 8) is called a dropdown menu.

Explanation:

🆕 New Concept Discovered: factoring sum and difference of cubes
Subtracting two perfect cube terms

Step 1: Analyze the terms of the expression

The given expression is:

$$ x^3 - 8 $$

Let's look at each term in the expression:

• The first term is \( x^3 \), which is the cube of \( x \) because \( (x)^3 = x^3 \).
• The second term is \( 8 \), which is a perfect cube because \( 2^3 = 2 \cdot 2 \cdot 2 = 8 \).

Step 2: Identify the mathematical structure

Since the expression consists of one perfect cube subtracted from another, it represents a subtraction of two cubes.

In algebra, an expression of the form \( a^3 - b^3 \) is called a difference of cubes (or difference of two cubes).

Answer:

difference of cubes