(6a%5E2%2B4ab-b%5E2).jpeg "(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
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Distribute the first term of the binomial:
(2a) * (6a^2+4ab-b^2) = 12a^3 + 8a^2b - 2ab^2
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Distribute the second term of the binomial:
(-3b) * (6a^2+4ab-b^2) = -18a^2b - 12ab^2 + 3b^3
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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.