(3a-%E2%80%93-1).jpeg "(2a2 + 5)(3a – 1)")
Expanding the Expression (2a² + 5)(3a – 1)
In mathematics, expanding an expression means removing the parentheses by applying the distributive property. This involves multiplying each term inside the first set of parentheses by each term in the second set of parentheses.
Let's expand the expression (2a² + 5)(3a – 1):
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Distribute the first term (2a²) from the first set of parentheses:
- (2a²) * (3a) = 6a³
- (2a²) * (-1) = -2a²
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Distribute the second term (5) from the first set of parentheses:
- (5) * (3a) = 15a
- (5) * (-1) = -5
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Combine all the terms:
- 6a³ - 2a² + 15a - 5
Therefore, the expanded form of (2a² + 5)(3a – 1) is 6a³ - 2a² + 15a - 5.
Key Points:
- Distributive Property: This is the fundamental concept used to expand the expression. It states that multiplying a sum by a number is the same as multiplying each addend in the sum by that number and adding the products.
- Combining Like Terms: After applying the distributive property, we combine like terms (terms with the same variable and exponent) to simplify the expression.
Example Application:
The expansion of (2a² + 5)(3a – 1) can be useful in solving equations, simplifying complex expressions, and in various other mathematical operations.