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

Jasonbradley

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Jun 16, 2024

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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.