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

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (3n-4)(4n^2+2n+3)

This article will explore the process of expanding the given expression, (3n-4)(4n^2+2n+3).

Understanding the Process

Expanding an expression like this involves using the distributive property. This means multiplying each term in the first factor by each term in the second factor.

Step-by-Step Expansion

1. Multiply the first term of the first factor (3n) by each term in the second factor:

   • 3n * 4n^2 = 12n^3
   • 3n * 2n = 6n^2
   • 3n * 3 = 9n

2. Multiply the second term of the first factor (-4) by each term in the second factor:

   • -4 * 4n^2 = -16n^2
   • -4 * 2n = -8n
   • -4 * 3 = -12

3. Combine all the resulting terms:

   • 12n^3 + 6n^2 + 9n - 16n^2 - 8n - 12

4. Simplify by combining like terms:

   • 12n^3 - 10n^2 + n - 12

Final Result

Therefore, the expanded form of the expression (3n-4)(4n^2+2n+3) is 12n^3 - 10n^2 + n - 12.

Conclusion

This process of expanding algebraic expressions is crucial for solving equations, simplifying complex expressions, and understanding the relationships between different mathematical expressions.