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Expanding the Expression: (x+3)(x^2-2x+4)
This article will guide you through the process of expanding the expression (x+3)(x^2-2x+4). We'll use the distributive property (also known as FOIL) to achieve this.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. In our case, we will distribute each term in the first set of parentheses, (x+3), over the terms in the second set of parentheses, (x^2-2x+4).
Expanding the Expression
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Multiply x by each term in the second parentheses:
- x * x^2 = x^3
- x * -2x = -2x^2
- x * 4 = 4x
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Multiply 3 by each term in the second parentheses:
- 3 * x^2 = 3x^2
- 3 * -2x = -6x
- 3 * 4 = 12
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Combine the results:
- x^3 - 2x^2 + 4x + 3x^2 - 6x + 12
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Simplify by combining like terms:
- x^3 + x^2 - 2x + 12
The Expanded Form
Therefore, the expanded form of (x+3)(x^2-2x+4) is x^3 + x^2 - 2x + 12.
Key Point
This expression is a special case, as (x^2 - 2x + 4) is a pattern that arises from the sum of cubes factorization. If you were to factor the expanded expression, you would arrive back at the original form.