(2x-1)^2-9x^2

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (2x-1)^2 - 9x^2

This article will guide you through simplifying the algebraic expression (2x-1)^2 - 9x^2. We'll break down the steps to arrive at the simplest form of this expression.

Understanding the Expression

The expression involves squaring a binomial (2x-1) and subtracting a term with a squared variable (9x^2). To simplify this, we'll need to use the following:

• Expanding Binomials: The square of a binomial can be expanded using the formula: (a - b)^2 = a^2 - 2ab + b^2
• Combining Like Terms: Terms with the same variable and exponent can be added or subtracted.

Step-by-Step Simplification

1. Expand the binomial:

   • Applying the formula to (2x-1)^2, we get: (2x)^2 - 2(2x)(1) + (1)^2 = 4x^2 - 4x + 1

2. Rewrite the expression:

   • Now our expression becomes: 4x^2 - 4x + 1 - 9x^2

3. Combine like terms:

   • Combine the x^2 terms: (4x^2 - 9x^2) = -5x^2
   • The remaining terms are already simplified.

4. Simplified expression:

   • The final simplified expression is: -5x^2 - 4x + 1

Conclusion

Therefore, the simplified form of the expression (2x-1)^2 - 9x^2 is -5x^2 - 4x + 1. This process demonstrates how to apply algebraic rules to simplify expressions involving binomials and squared variables.