(2x+3)(3x^2-6x+2)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (2x+3)(3x^2-6x+2)

This article will guide you through the process of expanding the expression (2x+3)(3x^2-6x+2).

Understanding the Problem

We are given a product of two expressions: (2x+3) and (3x^2-6x+2). Expanding this product means multiplying each term in the first expression by each term in the second expression and then simplifying the resulting expression.

Expanding the Expression

We can use the distributive property (or the FOIL method) to expand the expression.

1. Multiply the first term of the first expression (2x) by each term in the second expression:

   • 2x * 3x² = 6x³
   • 2x * -6x = -12x²
   • 2x * 2 = 4x

2. Multiply the second term of the first expression (3) by each term in the second expression:

   • 3 * 3x² = 9x²
   • 3 * -6x = -18x
   • 3 * 2 = 6

3. Combine the results from steps 1 and 2: 6x³ - 12x² + 4x + 9x² - 18x + 6

4. Combine like terms: 6x³ - 3x² - 14x + 6

Conclusion

Therefore, the expanded form of (2x+3)(3x^2-6x+2) is 6x³ - 3x² - 14x + 6.