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(2a-5)2+(9-2a)(9+2a)

2 min read Jun 16, 2024
(2a-5)2+(9-2a)(9+2a)

Simplifying the Expression: (2a-5)² + (9-2a)(9+2a)

This article will guide you through simplifying the given algebraic expression: (2a-5)² + (9-2a)(9+2a).

Understanding the Concepts

Before we start simplifying, let's recall some key algebraic concepts:

  • Squaring a binomial: (a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b²
  • Difference of squares: (a + b)(a - b) = a² - b²

Simplifying the Expression

Let's break down the simplification step-by-step:

  1. Expand (2a-5)²: Using the formula (a - b)² = a² - 2ab + b², we get: (2a-5)² = (2a)² - 2(2a)(5) + (5)² = 4a² - 20a + 25

  2. Expand (9-2a)(9+2a): Using the difference of squares formula, we get: (9-2a)(9+2a) = 9² - (2a)² = 81 - 4a²

  3. Combine the expanded terms: Now we have: (2a-5)² + (9-2a)(9+2a) = 4a² - 20a + 25 + 81 - 4a²

  4. Simplify by combining like terms: 4a² - 20a + 25 + 81 - 4a² = -20a + 106

Final Result

Therefore, the simplified form of the expression (2a-5)² + (9-2a)(9+2a) is -20a + 106.

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