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Expanding the Expression: (x+5)(x-1)(x+2)
This article will walk you through the process of expanding the given expression: (x+5)(x-1)(x+2).
Understanding the Process
Expanding an expression like this involves applying the distributive property multiple times. The distributive property states that a(b + c) = ab + ac.
In our case, we have three factors, so we'll apply the distributive property twice:
- First Expansion: Multiply the first two factors, (x+5) and (x-1).
- Second Expansion: Multiply the result of the first expansion by the third factor (x+2).
Step-by-Step Expansion
1. First Expansion:
- (x+5)(x-1) = x(x-1) + 5(x-1)
- = x² - x + 5x - 5
- = x² + 4x - 5
2. Second Expansion:
- (x² + 4x - 5)(x+2) = x²(x+2) + 4x(x+2) - 5(x+2)
- = x³ + 2x² + 4x² + 8x - 5x - 10
- = x³ + 6x² + 3x - 10
Conclusion
Therefore, the expanded form of the expression (x+5)(x-1)(x+2) is x³ + 6x² + 3x - 10.
This expanded form is a polynomial, specifically a cubic polynomial due to the highest power of x being 3. It can be used in various mathematical applications, including solving equations, finding roots, and analyzing the behavior of functions.