(2a-3b)(6a^2+4ab-b^2)

2 min read Jun 16, 2024
(2a-3b)(6a^2+4ab-b^2)

Multiplying Binomials and Trinomials: (2a-3b)(6a^2+4ab-b^2)

This article will guide you through the process of multiplying the binomial (2a-3b) by the trinomial (6a^2+4ab-b^2).

Understanding the Process

The multiplication of a binomial and a trinomial follows the distributive property. This means that each term in the binomial must be multiplied by every term in the trinomial.

Step-by-Step Solution

  1. Distribute the first term of the binomial:

    (2a) * (6a^2+4ab-b^2) = 12a^3 + 8a^2b - 2ab^2

  2. Distribute the second term of the binomial:

    (-3b) * (6a^2+4ab-b^2) = -18a^2b - 12ab^2 + 3b^3

  3. Combine like terms:

    12a^3 + 8a^2b - 2ab^2 - 18a^2b - 12ab^2 + 3b^3 = 12a^3 - 10a^2b - 14ab^2 + 3b^3

Final Result

Therefore, the product of (2a-3b) and (6a^2+4ab-b^2) is 12a^3 - 10a^2b - 14ab^2 + 3b^3.

Key Points to Remember

  • Always remember the distributive property when multiplying binomials and trinomials.
  • Pay attention to the signs of each term.
  • Combine like terms to simplify the final expression.

By following these steps, you can successfully multiply any binomial and trinomial.

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