(2a%5E2%2B6).jpeg "(8-3a^2)(2a^2+6)")
Expanding the Expression (8-3a^2)(2a^2+6)
This article will guide you through the process of expanding the given algebraic expression: (8-3a^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
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Multiply the first term of the first binomial by each term of the second binomial:
- 8 * 2a^2 = 16a^2
- 8 * 6 = 48
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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
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Combine all the resulting terms:
- 16a^2 + 48 - 6a^4 - 18a^2
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Rearrange the terms in descending order of their exponents:
- -6a^4 - 2a^2 + 48
Conclusion
Therefore, the expanded form of the expression (8-3a^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.