(2x%5E2-x-9).jpeg "(x+2)(2x^2-x-9)")
Expanding the Expression (x+2)(2x^2-x-9)
This article focuses on expanding the expression (x+2)(2x^2-x-9). We'll achieve this by applying the distributive property (also known as the FOIL method).
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend in the sum by that number and then adding the products.
In our case, we have two factors: (x+2) and (2x^2-x-9). To expand this expression, we need to multiply each term in the first factor by each term in the second factor.
Expanding the Expression
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Multiply x by each term in the second factor:
- x * (2x^2) = 2x^3
- x * (-x) = -x^2
- x * (-9) = -9x
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Multiply 2 by each term in the second factor:
- 2 * (2x^2) = 4x^2
- 2 * (-x) = -2x
- 2 * (-9) = -18
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Combine all the terms:
- 2x^3 - x^2 - 9x + 4x^2 - 2x - 18
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Simplify by combining like terms:
- 2x^3 + 3x^2 - 11x - 18
Conclusion
Therefore, the expanded form of (x+2)(2x^2-x-9) is 2x^3 + 3x^2 - 11x - 18. This process involves applying the distributive property and then simplifying the resulting expression by combining like terms.