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(3n+4)^2-(3n+2)^2/10n+10

2 min read Jun 16, 2024
(3n+4)^2-(3n+2)^2/10n+10

Simplifying the Expression (3n+4)^2 - (3n+2)^2 / 10n+10

This article will guide you through simplifying the expression: (3n+4)^2 - (3n+2)^2 / 10n+10

Understanding the Expression

The expression involves several operations:

  • Squaring: (3n+4)^2 and (3n+2)^2
  • Subtraction: (3n+4)^2 - (3n+2)^2
  • Division: The result of the subtraction is divided by 10n+10

Simplifying the Expression

  1. Expand the Squares:

    • (3n+4)^2 = (3n+4)(3n+4) = 9n^2 + 24n + 16
    • (3n+2)^2 = (3n+2)(3n+2) = 9n^2 + 12n + 4

  2. Substitute the Expanded Forms:

    • (3n+4)^2 - (3n+2)^2 / 10n+10 becomes
    • (9n^2 + 24n + 16) - (9n^2 + 12n + 4) / 10n+10

  3. Simplify the Subtraction:

    • 9n^2 + 24n + 16 - 9n^2 - 12n - 4 = 12n + 12

  4. Factor out the Common Factor:

    • 12n + 12 = 12(n + 1)

  5. Simplify the Division:

    • 12(n + 1) / 10n + 10 = (12(n + 1)) / (10(n + 1))

  6. Cancel Common Factors:

    • (12(n + 1)) / (10(n + 1)) = 12/10

  7. Final Simplification:

    • 12/10 = 6/5

Conclusion

The simplified expression for (3n+4)^2 - (3n+2)^2 / 10n+10 is 6/5. This simplification process involves applying the order of operations and utilizing algebraic techniques like expansion, subtraction, factoring, and cancellation of common factors.

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