(3x^3-9x+7)(x^2-2x+1)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (3x^3 - 9x + 7)(x^2 - 2x + 1)

This article will guide you through expanding the expression (3x^3 - 9x + 7)(x^2 - 2x + 1). We will use the distributive property to multiply each term in the first polynomial by each term in the second polynomial.

Step-by-Step Solution

1. Distribute the first term of the first polynomial (3x^3) across the second polynomial:

   3x^3 * (x^2 - 2x + 1) = 3x^5 - 6x^4 + 3x^3
   

2. Distribute the second term of the first polynomial (-9x) across the second polynomial:

   -9x * (x^2 - 2x + 1) = -9x^3 + 18x^2 - 9x
   

3. Distribute the third term of the first polynomial (7) across the second polynomial:

   7 * (x^2 - 2x + 1) = 7x^2 - 14x + 7
   

4. Combine all the resulting terms:

   (3x^5 - 6x^4 + 3x^3) + (-9x^3 + 18x^2 - 9x) + (7x^2 - 14x + 7) 
   

5. Simplify by combining like terms:

   3x^5 - 6x^4 - 6x^3 + 25x^2 - 23x + 7
   

Final Result

Therefore, the expanded form of the expression (3x^3 - 9x + 7)(x^2 - 2x + 1) is 3x^5 - 6x^4 - 6x^3 + 25x^2 - 23x + 7.