(2-a)(3a^2+3a-5)

Jasonbradley

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Jun 16, 2024

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Multiplying Binomials and Trinomials: (2-a)(3a^2+3a-5)

This article will guide you through the process of multiplying a binomial (2-a) by a trinomial (3a^2+3a-5). We will use the distributive property to achieve this.

The Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the products together. In simpler terms:

a(b + c) = ab + ac

Applying the Distributive Property

1. Multiply the first term of the binomial (2) by each term of the trinomial:

   • 2 * 3a^2 = 6a^2
   • 2 * 3a = 6a
   • 2 * -5 = -10

2. Multiply the second term of the binomial (-a) by each term of the trinomial:

   • -a * 3a^2 = -3a^3
   • -a * 3a = -3a^2
   • -a * -5 = 5a

3. Combine all the results:

   • 6a^2 + 6a - 10 - 3a^3 - 3a^2 + 5a

4. Simplify by combining like terms:

   • -3a^3 + 3a^2 + 11a - 10

Final Result

Therefore, the product of (2-a) and (3a^2+3a-5) is -3a^3 + 3a^2 + 11a - 10.