(5x+2)(x^2-3x+6) Answer

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (5x+2)(x^2-3x+6)

This article will guide you through the process of expanding the expression (5x+2)(x^2-3x+6).

Understanding the Concept

The given expression is a product of two polynomials. To expand it, we need to apply the distributive property (also known as the FOIL method) which involves multiplying each term of the first polynomial by each term of the second polynomial.

Steps to Expand the Expression

1. Multiply the first term of the first polynomial by each term of the second polynomial:

   • 5x * x^2 = 5x^3
   • 5x * -3x = -15x^2
   • 5x * 6 = 30x

2. Multiply the second term of the first polynomial by each term of the second polynomial:

   • 2 * x^2 = 2x^2
   • 2 * -3x = -6x
   • 2 * 6 = 12

3. Combine all the resulting terms:

   • 5x^3 - 15x^2 + 30x + 2x^2 - 6x + 12

4. Simplify by combining like terms:

   • 5x^3 - 13x^2 + 24x + 12

Final Result

Therefore, the expanded form of the expression (5x+2)(x^2-3x+6) is 5x^3 - 13x^2 + 24x + 12.