(x-1)^3 Simplify

Jasonbradley

2 min read

·

Jun 17, 2024

16

Share

Simplifying (x-1)³

In algebra, simplifying expressions is a crucial skill. One common expression that often requires simplification is (x-1)³. This article will guide you through the steps involved in simplifying this expression.

Understanding the Concept

(x-1)³ essentially means multiplying (x-1) by itself three times: (x-1) * (x-1) * (x-1). To simplify this, we'll use the distributive property and some algebraic rules.

Step-by-Step Simplification

1. Expand the first two terms:
   (x-1) * (x-1) = x² - x - x + 1 = x² - 2x + 1

2. Multiply the result by (x-1): (x² - 2x + 1) * (x-1) = x³ - 2x² + x - x² + 2x - 1

3. Combine like terms: x³ - 2x² + x - x² + 2x - 1 = x³ - 3x² + 3x - 1

Final Result

Therefore, the simplified form of (x-1)³ is x³ - 3x² + 3x - 1.

Key Takeaways

• Distributive property: This is the foundation of expanding the expression.
• Combining like terms: This helps to simplify the expression to its most concise form.
• Understanding exponents: Knowing what (x-1)³ represents is essential for the simplification process.

By following these steps, you can successfully simplify expressions like (x-1)³ and confidently apply this knowledge in various algebraic problems.