(3a+1)(5a^2+2a-6)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (3a+1)(5a^2+2a-6)

This article will guide you through the process of expanding the given expression: (3a+1)(5a^2+2a-6).

Understanding the Concept

Expanding an expression of this form involves applying the distributive property. This property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products together.

Steps for Expansion

1. Distribute the first term: We start by multiplying the first term of the first binomial (3a) by each term of the second binomial:

   (3a)(5a^2) + (3a)(2a) + (3a)(-6)

2. Distribute the second term: Now, we multiply the second term of the first binomial (1) by each term of the second binomial:

   (1)(5a^2) + (1)(2a) + (1)(-6)

3. Combine the terms: Combine all the terms obtained in the previous steps:

   15a^3 + 6a^2 - 18a + 5a^2 + 2a - 6

4. Simplify: Finally, combine like terms to get the expanded form:

   15a^3 + 11a^2 - 16a - 6

Conclusion

Therefore, the expanded form of the expression (3a+1)(5a^2+2a-6) is 15a^3 + 11a^2 - 16a - 6. This process demonstrates the application of the distributive property to simplify and expand algebraic expressions.