-%2B-(x2-%E2%88%92-x-%E2%88%92-27)-%E2%88%92-(x-%2B-5)(x-%E2%88%92-7).jpeg "(4x2 + 8x + 15) + (x2 − X − 27) − (x + 5)(x − 7)")
Simplifying the Expression: (4x² + 8x + 15) + (x² − x − 27) − (x + 5)(x − 7)
This problem involves combining multiple algebraic expressions. To simplify it, we'll follow these steps:
1. Expand the Product
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First, we need to expand the product (x + 5)(x − 7) using the FOIL method (First, Outer, Inner, Last):
- First: x * x = x²
- Outer: x * -7 = -7x
- Inner: 5 * x = 5x
- Last: 5 * -7 = -35
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Combining these terms gives us: x² - 7x + 5x - 35 = x² - 2x - 35
2. Combine Like Terms
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Now, we can rewrite the entire expression: (4x² + 8x + 15) + (x² − x − 27) − (x² - 2x - 35)
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Combining like terms (terms with the same variable and exponent):
- x² terms: 4x² + x² - x² = 4x²
- x terms: 8x - x + 2x = 9x
- Constant terms: 15 - 27 + 35 = 23
3. Simplified Expression
- Combining all the terms, we get the simplified expression: 4x² + 9x + 23
Therefore, the simplified form of the given expression (4x² + 8x + 15) + (x² − x − 27) − (x + 5)(x − 7) is 4x² + 9x + 23.