(6a2-%E2%88%92-a-%2B-2).jpeg "(4a + 2)(6a2 − A + 2)")
Expanding the Expression (4a + 2)(6a² − a + 2)
This article will guide you through the process of expanding the expression (4a + 2)(6a² − a + 2) using the distributive property.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. In simpler terms:
a(b + c) = ab + ac
Applying the Distributive Property to Our Expression
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Distribute (4a) over the entire second expression: (4a + 2)(6a² − a + 2) = 4a(6a² − a + 2) + 2(6a² − a + 2)
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Distribute (2) over the entire second expression: = 4a(6a² − a + 2) + 2(6a² − a + 2)
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Multiply each term within the parentheses: = 24a³ - 4a² + 8a + 12a² - 2a + 4
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Combine like terms: = 24a³ + 8a² + 6a + 4
Final Result
Therefore, the expanded form of (4a + 2)(6a² − a + 2) is 24a³ + 8a² + 6a + 4.
Key Takeaways
- The distributive property is a fundamental tool for simplifying algebraic expressions.
- By applying the distributive property step-by-step, you can expand complex expressions into simpler ones.
- Combining like terms after expanding is crucial to obtaining the final simplified result.