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Expanding the Expression (x+4)(x^2-5x+9)
This article will guide you through the process of expanding the expression (x+4)(x^2-5x+9).
Understanding the Process
The expression is in the form of two factors being multiplied together. To expand it, we will use the distributive property. This means multiplying each term in the first factor with each term in the second factor.
Steps to Expand
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Multiply the first term of the first factor (x) with each term in the second factor:
- x * x^2 = x^3
- x * -5x = -5x^2
- x * 9 = 9x
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Multiply the second term of the first factor (4) with each term in the second factor:
- 4 * x^2 = 4x^2
- 4 * -5x = -20x
- 4 * 9 = 36
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Combine all the resulting terms:
- x^3 - 5x^2 + 9x + 4x^2 - 20x + 36
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Simplify by combining like terms:
- x^3 - x^2 - 11x + 36
Final Result
Therefore, the expanded form of (x+4)(x^2-5x+9) is x^3 - x^2 - 11x + 36.
Importance of Expanding Expressions
Expanding expressions like this is crucial in many areas of mathematics, including:
- Solving equations: Expanding can help simplify equations and make them easier to solve.
- Calculus: Expanding is a key step in finding derivatives and integrals of functions.
- Algebraic manipulation: Expanding expressions is often necessary for simplifying and manipulating other algebraic expressions.
By understanding the process of expanding expressions, you gain a powerful tool for solving problems and working with algebraic equations.