(x+1)(3x^2+9x+2)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (x+1)(3x^2+9x+2)

This article explores the process of expanding the expression (x+1)(3x^2+9x+2), a common task in algebra.

Understanding the Process

Expanding this expression involves multiplying each term within the first set of parentheses by each term within the second set of parentheses. This is based on the distributive property of multiplication.

Step-by-Step Expansion

1. Multiply x by each term in the second set of parentheses:

   • x * 3x^2 = 3x^3
   • x * 9x = 9x^2
   • x * 2 = 2x

2. Multiply 1 by each term in the second set of parentheses:

   • 1 * 3x^2 = 3x^2
   • 1 * 9x = 9x
   • 1 * 2 = 2

3. Combine all the resulting terms:

   • 3x^3 + 9x^2 + 2x + 3x^2 + 9x + 2

4. Simplify by combining like terms:

   • 3x^3 + (9x^2 + 3x^2) + (2x + 9x) + 2

5. Final Result:

   • 3x^3 + 12x^2 + 11x + 2

Conclusion

Therefore, the expanded form of the expression (x+1)(3x^2+9x+2) is 3x^3 + 12x^2 + 11x + 2. This process demonstrates the application of the distributive property and how it is used to simplify algebraic expressions.