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

Distribute the first term of the first factor (7k):
(7k)(k²  2k + 7) = 7k³  14k² + 49k

Distribute the second term of the first factor (3):
(3)(k²  2k + 7) = 3k² + 6k  21

Combine the results:
7k³  14k² + 49k  3k² + 6k  21

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.