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Expanding (x-9)(x+2)
In mathematics, expanding expressions is a fundamental process that involves simplifying algebraic expressions. One common type of expansion involves multiplying binomials. In this case, we'll explore the expansion of the expression (x-9)(x+2).
Understanding the Process
To expand this expression, we'll utilize the distributive property (also known as FOIL - First, Outer, Inner, Last). This property states that the product of two binomials is equal to the sum of the products of each term in the first binomial with each term in the second binomial.
Steps for Expansion
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First: Multiply the first terms of each binomial:
x * x = x² -
Outer: Multiply the outer terms of the binomials: x * 2 = 2x
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Inner: Multiply the inner terms of the binomials: -9 * x = -9x
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Last: Multiply the last terms of the binomials: -9 * 2 = -18
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Combine: Add all the resulting terms: x² + 2x - 9x - 18
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Simplify: Combine like terms: x² - 7x - 18
Final Result
Therefore, the expanded form of (x-9)(x+2) is x² - 7x - 18.
Applications
Expanding expressions like this one is a crucial step in many mathematical concepts, including:
- Solving quadratic equations: Expanding the expression can help determine the roots of the equation.
- Graphing quadratic functions: The expanded form allows us to identify the vertex and intercepts of the parabola representing the function.
- Factoring polynomials: Understanding expansion helps us reverse the process to factor expressions into simpler binomials.
Understanding the process of expanding binomials is essential for a strong foundation in algebra and its applications in various mathematical and scientific fields.