Jasonbradley
Home

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

3 min read Jun 16, 2024
(3x^4-2x^3-2x^2+4x-8) (x^2-2)

Multiplying Polynomials: (3x^4 - 2x^3 - 2x^2 + 4x - 8)(x^2 - 2)

This article will guide you through the process of multiplying two polynomials: (3x^4 - 2x^3 - 2x^2 + 4x - 8) and (x^2 - 2). We will use the distributive property 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 by the number and then adding the products. In our case, we need to multiply each term of the first polynomial by each term of the second polynomial.

Step-by-Step Solution

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

    (3x^4)(x^2) + (3x^4)(-2) = 3x^6 - 6x^4

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

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

  3. Multiply the third term of the first polynomial by each term of the second polynomial:

    (-2x^2)(x^2) + (-2x^2)(-2) = -2x^4 + 4x^2

  4. Multiply the fourth term of the first polynomial by each term of the second polynomial:

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

  5. Multiply the fifth term of the first polynomial by each term of the second polynomial:

    (-8)(x^2) + (-8)(-2) = -8x^2 + 16

  6. Add all the resulting terms:

    3x^6 - 6x^4 - 2x^5 + 4x^3 - 2x^4 + 4x^2 + 4x^3 - 8x - 8x^2 + 16

  7. Combine like terms:

    3x^6 - 2x^5 - 8x^4 + 8x^3 - 4x^2 - 8x + 16

Conclusion

Therefore, the product of (3x^4 - 2x^3 - 2x^2 + 4x - 8) and (x^2 - 2) is 3x^6 - 2x^5 - 8x^4 + 8x^3 - 4x^2 - 8x + 16.

Related Post

Featured Posts