(x%2B1)(3x%E2%88%925).jpeg "(2x+5)(x+1)(3x−5)")
Expanding and Simplifying the Expression: (2x+5)(x+1)(3x-5)
This article will guide you through the process of expanding and simplifying the given expression: (2x+5)(x+1)(3x-5).
Expanding the Expression
To simplify the expression, we need to expand it. We can do this by multiplying the terms together step by step:
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Start with the first two factors: (2x+5)(x+1)
- Apply the distributive property (or FOIL method): (2x+5)(x+1) = 2x(x+1) + 5(x+1)
- Simplify: 2x² + 2x + 5x + 5 = 2x² + 7x + 5
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Now multiply the result from step 1 with the third factor: (2x² + 7x + 5)(3x-5)
- Apply the distributive property again: (2x² + 7x + 5)(3x-5) = 2x²(3x-5) + 7x(3x-5) + 5(3x-5)
- Simplify: 6x³ - 10x² + 21x² - 35x + 15x - 25
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Combine like terms: 6x³ + 11x² - 20x - 25
The Simplified Expression
Therefore, the expanded and simplified form of the expression (2x+5)(x+1)(3x-5) is 6x³ + 11x² - 20x - 25.