(x-1)^3 Simplify

2 min read Jun 17, 2024
(x-1)^3 Simplify

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.

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