(2x^4-4x^3+5x^2+2x-3) (2x^2-1)

Jasonbradley

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Jun 16, 2024

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Multiplying Polynomials: (2x^4 - 4x^3 + 5x^2 + 2x - 3)(2x^2 - 1)

This article will demonstrate how to multiply the two polynomials (2x^4 - 4x^3 + 5x^2 + 2x - 3) and (2x^2 - 1) using the distributive property.

Understanding the Distributive Property

The distributive property states that to multiply a sum by a number, we multiply each term of the sum by that number. For polynomials, we apply the distributive property repeatedly.

Multiplication Process

1. Distribute the first term of the second polynomial: (2x^2 - 1) * (2x^4 - 4x^3 + 5x^2 + 2x - 3) = 2x^2 * (2x^4 - 4x^3 + 5x^2 + 2x - 3) - 1 * (2x^4 - 4x^3 + 5x^2 + 2x - 3)

2. Distribute the first term of the second polynomial: = 4x^6 - 8x^5 + 10x^4 + 4x^3 - 6x^2 - (2x^4 - 4x^3 + 5x^2 + 2x - 3)

3. Distribute the negative sign: = 4x^6 - 8x^5 + 10x^4 + 4x^3 - 6x^2 - 2x^4 + 4x^3 - 5x^2 - 2x + 3

4. Combine like terms: = 4x^6 - 8x^5 + 8x^4 + 8x^3 - 11x^2 - 2x + 3

Final Result

Therefore, the product of (2x^4 - 4x^3 + 5x^2 + 2x - 3) and (2x^2 - 1) is 4x^6 - 8x^5 + 8x^4 + 8x^3 - 11x^2 - 2x + 3.