(5x%5E2-6x%2B1).jpeg "(x^2+5x-1)(5x^2-6x+1)")
Expanding the Expression (x^2 + 5x - 1)(5x^2 - 6x + 1)
This article will guide you through the process of expanding the given expression: (x^2 + 5x - 1)(5x^2 - 6x + 1). We will achieve this by utilizing the distributive property of multiplication.
Expanding the Expression
The distributive property states that for any numbers a, b, and c:
- a(b + c) = ab + ac
To expand our expression, we'll treat each term in the first set of parentheses as a separate multiplier and multiply it by each term in the second set of parentheses.
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Multiply x^2 by each term in the second set of parentheses:
- x^2 * (5x^2 - 6x + 1) = 5x^4 - 6x^3 + x^2
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Multiply 5x by each term in the second set of parentheses:
- 5x * (5x^2 - 6x + 1) = 25x^3 - 30x^2 + 5x
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Multiply -1 by each term in the second set of parentheses:
- -1 * (5x^2 - 6x + 1) = -5x^2 + 6x - 1
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Combine all the resulting terms:
- 5x^4 - 6x^3 + x^2 + 25x^3 - 30x^2 + 5x - 5x^2 + 6x - 1
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Simplify by combining like terms:
- 5x^4 + 19x^3 - 34x^2 + 11x - 1
Conclusion
Therefore, the expanded form of (x^2 + 5x - 1)(5x^2 - 6x + 1) is 5x^4 + 19x^3 - 34x^2 + 11x - 1. This method of expanding expressions is crucial for understanding and manipulating polynomial functions in various mathematical contexts.