(2x+3)(2x-3)-(2x+3)^2

2 min read Jun 16, 2024
(2x+3)(2x-3)-(2x+3)^2

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

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

Understanding the Expression

The expression involves two operations:

  • Multiplication: (2x+3)(2x-3) and (2x+3)^2
  • Subtraction: Subtracting the result of the second multiplication from the result of the first.

Simplifying the Expression Step-by-Step

  1. Expand (2x+3)(2x-3) using the difference of squares pattern:

    • (a+b)(a-b) = a^2 - b^2
    • Therefore, (2x+3)(2x-3) = (2x)^2 - (3)^2 = 4x^2 - 9
  2. Expand (2x+3)^2 using the square of a binomial pattern:

    • (a+b)^2 = a^2 + 2ab + b^2
    • Therefore, (2x+3)^2 = (2x)^2 + 2(2x)(3) + (3)^2 = 4x^2 + 12x + 9
  3. Substitute the simplified expressions back into the original expression:

    • (2x+3)(2x-3)-(2x+3)^2 = (4x^2 - 9) - (4x^2 + 12x + 9)
  4. Distribute the negative sign:

    • 4x^2 - 9 - 4x^2 - 12x - 9
  5. Combine like terms:

    • (4x^2 - 4x^2) - 12x + (-9 - 9) = -12x - 18

Final Result

Therefore, the simplified form of the expression (2x+3)(2x-3)-(2x+3)^2 is -12x - 18.

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