(-x^2+5x-3)(x^8-4x^3+5)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (-x^2 + 5x - 3)(x^8 - 4x^3 + 5)

This article will guide you through the process of expanding the given expression: (-x^2 + 5x - 3)(x^8 - 4x^3 + 5). We will use the distributive property, also known as the FOIL method, to achieve this.

Understanding the Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend of the sum by the number and then adding the results. In our case, we have two trinomials:

• (-x^2 + 5x - 3)
• (x^8 - 4x^3 + 5)

We will multiply each term in the first trinomial by every term in the second trinomial.

Expanding the Expression

1. Multiply -x^2 by each term in the second trinomial:

   • (-x^2) * (x^8) = -x^10
   • (-x^2) * (-4x^3) = 4x^5
   • (-x^2) * (5) = -5x^2

2. Multiply 5x by each term in the second trinomial:

   • (5x) * (x^8) = 5x^9
   • (5x) * (-4x^3) = -20x^4
   • (5x) * (5) = 25x

3. Multiply -3 by each term in the second trinomial:

   • (-3) * (x^8) = -3x^8
   • (-3) * (-4x^3) = 12x^3
   • (-3) * (5) = -15

4. Combine all the resulting terms:

   -x^10 + 4x^5 - 5x^2 + 5x^9 - 20x^4 + 25x - 3x^8 + 12x^3 - 15

5. Arrange the terms in descending order of their exponents:

   -x^10 + 5x^9 - 3x^8 - 20x^4 + 4x^5 + 12x^3 - 5x^2 + 25x - 15

Final Result

The expanded form of the expression (-x^2 + 5x - 3)(x^8 - 4x^3 + 5) is:

-x^10 + 5x^9 - 3x^8 - 20x^4 + 4x^5 + 12x^3 - 5x^2 + 25x - 15