(2a%5E2-5a%2B3).jpeg "(7a+2)(2a^2-5a+3)")
Expanding the Expression (7a + 2)(2a² - 5a + 3)
This article will guide you through the process of expanding the expression (7a + 2)(2a² - 5a + 3).
Understanding the Concept
Expanding an expression like this involves multiplying each term in the first set of parentheses by each term in the second set of parentheses. This is commonly referred to as the distributive property.
The Steps
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Distribute the first term of the first set of parentheses:
- Multiply 7a by each term in the second set:
- 7a * 2a² = 14a³
- 7a * -5a = -35a²
- 7a * 3 = 21a
- Multiply 7a by each term in the second set:
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Distribute the second term of the first set of parentheses:
- Multiply 2 by each term in the second set:
- 2 * 2a² = 4a²
- 2 * -5a = -10a
- 2 * 3 = 6
- Multiply 2 by each term in the second set:
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Combine the results:
- 14a³ - 35a² + 21a + 4a² - 10a + 6
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Simplify by combining like terms:
- 14a³ - 31a² + 11a + 6
The Expanded Form
Therefore, the expanded form of (7a + 2)(2a² - 5a + 3) is 14a³ - 31a² + 11a + 6.
Conclusion
Expanding expressions like this is a fundamental skill in algebra. Understanding the distributive property and following the steps outlined above will help you confidently expand any similar expression.