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(x-1)2-(x+3)(x-3)

less than a minute read Jun 17, 2024
(x-1)2-(x+3)(x-3)

Simplifying the Expression (x-1)² - (x+3)(x-3)

This article will guide you through the process of simplifying the algebraic expression (x-1)² - (x+3)(x-3).

Understanding the Concepts

Before we begin, let's refresh some important algebraic concepts:

  • Squaring a Binomial: (a + b)² = a² + 2ab + b²
  • Difference of Squares: (a + b)(a - b) = a² - b²

Simplifying the Expression

  1. Expand the first term: (x - 1)² = x² - 2x + 1

  2. Expand the second term (using Difference of Squares): (x + 3)(x - 3) = x² - 9

  3. Substitute the expanded terms back into the original expression: x² - 2x + 1 - (x² - 9)

  4. Distribute the negative sign: x² - 2x + 1 - x² + 9

  5. Combine like terms: -2x + 10

Final Result

Therefore, the simplified form of the expression (x-1)² - (x+3)(x-3) is -2x + 10.

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