-(x%2B1).jpeg "(x^3-2x^2+5x+8) (x+1)")
Expanding the Expression (x³ - 2x² + 5x + 8)(x + 1)
This article aims to guide you through the process of expanding the given expression: (x³ - 2x² + 5x + 8)(x + 1).
Understanding the Process
The expansion involves applying the distributive property, also known as the FOIL method (First, Outer, Inner, Last) for multiplying two binomials. In this case, we need to multiply each term in the first polynomial (x³ - 2x² + 5x + 8) by each term in the second polynomial (x + 1).
Step-by-Step Expansion
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Multiply x³ by each term in (x + 1):
- x³ * x = x⁴
- x³ * 1 = x³
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Multiply -2x² by each term in (x + 1):
- -2x² * x = -2x³
- -2x² * 1 = -2x²
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Multiply 5x by each term in (x + 1):
- 5x * x = 5x²
- 5x * 1 = 5x
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Multiply 8 by each term in (x + 1):
- 8 * x = 8x
- 8 * 1 = 8
Combining Like Terms
Now, we add all the resulting terms together and combine like terms:
x⁴ + x³ - 2x³ - 2x² + 5x² + 5x + 8x + 8
Simplified: x⁴ - x³ + 3x² + 13x + 8
Final Result
Therefore, the expanded form of the expression (x³ - 2x² + 5x + 8)(x + 1) is x⁴ - x³ + 3x² + 13x + 8.