Expanding the Expression (83a^2)(2a^2+6)
This article will guide you through the process of expanding the given algebraic expression: (83a^2)(2a^2+6).
Understanding the Process
Expanding an expression like this involves using the distributive property of multiplication. This property states that to multiply a sum by a number, we multiply each term of the sum by the number separately and then add the results.
Expanding the Expression

Multiply the first term of the first binomial by each term of the second binomial:
 8 * 2a^2 = 16a^2
 8 * 6 = 48

Multiply the second term of the first binomial by each term of the second binomial:
 3a^2 * 2a^2 = 6a^4
 3a^2 * 6 = 18a^2

Combine all the resulting terms:
 16a^2 + 48  6a^4  18a^2

Rearrange the terms in descending order of their exponents:
 6a^4  2a^2 + 48
Conclusion
Therefore, the expanded form of the expression (83a^2)(2a^2+6) is 6a^4  2a^2 + 48. Remember that when expanding expressions, it's important to apply the distributive property carefully and combine like terms to simplify the result.