(%E2%88%923a2%2B5).jpeg "(3a2−1)(−3a2+5)")
Expanding the Expression (3a² - 1)(-3a² + 5)
This article will guide you through the steps of expanding the expression (3a² - 1)(-3a² + 5).
Understanding the Process
Expanding the expression means multiplying each term within the first set of parentheses by each term within the second set of parentheses. We will be using the distributive property for this purpose.
Expanding the Expression
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Start by multiplying the first term of the first set of parentheses by each term in the second set of parentheses: (3a²) * (-3a²) + (3a²) * (5)
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Next, multiply the second term of the first set of parentheses by each term in the second set of parentheses: (-1) * (-3a²) + (-1) * (5)
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Combine all the terms: -9a⁴ + 15a² + 3a² - 5
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Finally, combine like terms: -9a⁴ + 18a² - 5
The Expanded Form
Therefore, the expanded form of (3a² - 1)(-3a² + 5) is -9a⁴ + 18a² - 5.
Key Points to Remember
- Distributive Property: The distributive property is the key to expanding expressions. It states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
- Combining Like Terms: After expanding, remember to combine like terms to simplify the expression.
By following these steps, you can confidently expand expressions like (3a² - 1)(-3a² + 5).