(k%5E2-2k%2B7).jpeg "(7k-3)(k^2-2k+7)")
Expanding the Expression (7k - 3)(k² - 2k + 7)
This article will guide you through the process of expanding the expression (7k - 3)(k² - 2k + 7). We'll use the distributive property (also known as FOIL) to simplify this expression.
Understanding the Distributive Property
The distributive property states that for any numbers a, b, and c:
a (b + c) = ab + ac
We can apply this property to expand our expression.
Expanding the Expression
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Distribute the first term of the first factor (7k):
(7k)(k² - 2k + 7) = 7k³ - 14k² + 49k
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Distribute the second term of the first factor (-3):
(-3)(k² - 2k + 7) = -3k² + 6k - 21
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Combine the results:
7k³ - 14k² + 49k - 3k² + 6k - 21
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Simplify by combining like terms:
7k³ - 17k² + 55k - 21
Conclusion
Therefore, the expanded form of the expression (7k - 3)(k² - 2k + 7) is 7k³ - 17k² + 55k - 21. This process utilizes the distributive property, a fundamental concept in algebra, to simplify expressions.