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Expanding (x+9)(x+1)
The expression (x+9)(x+1) represents the product of two binomials. To expand it, we can use the FOIL method:
First: Multiply the first terms of each binomial: x * x = x² Outer: Multiply the outer terms of the binomials: x * 1 = x Inner: Multiply the inner terms of the binomials: 9 * x = 9x Last: Multiply the last terms of each binomial: 9 * 1 = 9
Now, we combine the terms:
x² + x + 9x + 9
Finally, we simplify by combining like terms:
x² + 10x + 9
Therefore, the expanded form of (x+9)(x+1) is x² + 10x + 9.
Understanding the Process
The FOIL method helps us systematically multiply each term in the first binomial with each term in the second binomial. It ensures that we don't miss any terms during multiplication.
This expansion process is essential for various mathematical operations, including:
- Solving quadratic equations: The expanded form helps us factorize the equation and find its roots.
- Graphing quadratic functions: The expanded form allows us to identify the vertex, axis of symmetry, and intercepts of the parabola represented by the function.
- Simplifying expressions: The expanded form simplifies complex expressions and makes them easier to work with.
Conclusion
Expanding (x+9)(x+1) using the FOIL method is a fundamental skill in algebra. It allows us to manipulate and simplify expressions, which is essential for solving equations, graphing functions, and performing various other mathematical operations. Understanding this process helps build a strong foundation for more advanced mathematical concepts.