(6a-2-%E2%88%92-a-%2B-2).jpeg "(4a + 2)(6a 2 − A + 2)")
Expanding the Expression (4a + 2)(6a² - a + 2)
This article will guide you through 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 separately by the number and then adding the products. In symbols, this is represented as:
a(b + c) = ab + ac
Applying the Distributive Property
To expand (4a + 2)(6a² - a + 2), we can think of it as:
4a(6a² - a + 2) + 2(6a² - a + 2)
Now, we apply the distributive property to each term:
- 4a(6a² - a + 2) = 24a³ - 4a² + 8a
- 2(6a² - a + 2) = 12a² - 2a + 4
Finally, we combine the like terms:
24a³ - 4a² + 8a + 12a² - 2a + 4
This simplifies to:
24a³ + 8a² + 6a + 4
Conclusion
Therefore, the expanded form of (4a + 2)(6a² - a + 2) is 24a³ + 8a² + 6a + 4. This process showcases the importance of understanding the distributive property and applying it to simplify complex expressions.