(6a%5E2---a-%2B-2).jpeg "(4a + 2)(6a^2 - A + 2)")
Expanding the Expression (4a + 2)(6a^2 - a + 2)
This article will guide you through expanding the expression (4a + 2)(6a^2 - a + 2) using the distributive property (often referred to as FOIL).
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 results. In simpler terms, we can distribute a term to each term within parentheses.
Applying the Distributive Property
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Multiply the first term of the first binomial by each term of the second binomial:
- 4a * 6a^2 = 24a^3
- 4a * -a = -4a^2
- 4a * 2 = 8a
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Multiply the second term of the first binomial by each term of the second binomial:
- 2 * 6a^2 = 12a^2
- 2 * -a = -2a
- 2 * 2 = 4
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Combine all the results: 24a^3 - 4a^2 + 8a + 12a^2 - 2a + 4
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Simplify by combining like terms: 24a^3 + 8a^2 + 6a + 4
Final Expanded Form
Therefore, the expanded form of the expression (4a + 2)(6a^2 - a + 2) is 24a^3 + 8a^2 + 6a + 4.
Conclusion
By applying the distributive property, we successfully expanded the expression and simplified it to its final form. This method can be applied to any binomial multiplication and is a fundamental tool in algebra.