(x%5E2-10x%2B2).jpeg "(3x+5)(x^2-10x+2)")
Expanding the Expression (3x+5)(x^2-10x+2)
This article will guide you through expanding the expression (3x+5)(x^2-10x+2). This process involves applying the distributive property, often referred to as FOIL (First, Outer, Inner, Last) for binomials.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend separately by that number and then adding the products. In our case, we'll apply this to both terms of (3x+5) to each term of (x^2-10x+2).
Expanding the Expression
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Multiply 3x by each term in the second parenthesis:
- 3x * x^2 = 3x^3
- 3x * -10x = -30x^2
- 3x * 2 = 6x
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Multiply 5 by each term in the second parenthesis:
- 5 * x^2 = 5x^2
- 5 * -10x = -50x
- 5 * 2 = 10
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Combine the results:
- 3x^3 - 30x^2 + 6x + 5x^2 - 50x + 10
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Simplify by combining like terms:
- 3x^3 - 25x^2 - 44x + 10
Final Result
Therefore, the expanded form of the expression (3x+5)(x^2-10x+2) is 3x^3 - 25x^2 - 44x + 10.
This method can be applied to any similar expression involving the product of two polynomials. Remember to apply the distributive property carefully and combine like terms for a simplified result.