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Expanding the Expression: (2x+1)(x+9)
In mathematics, expanding an expression means removing the parentheses by applying the distributive property. Let's explore how to expand the expression (2x+1)(x+9):
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 twice to expand our expression.
Expanding (2x+1)(x+9)
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Distribute (2x+1) over (x+9): (2x+1)(x+9) = 2x(x+9) + 1(x+9)
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Distribute 2x and 1: 2x(x+9) + 1(x+9) = 2x² + 18x + x + 9
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Combine like terms: 2x² + 18x + x + 9 = 2x² + 19x + 9
Therefore, the expanded form of (2x+1)(x+9) is 2x² + 19x + 9.
Applications
Expanding expressions like (2x+1)(x+9) is fundamental in algebra and has various applications, including:
- Solving equations: Expanding the expression might be necessary to solve quadratic equations.
- Graphing functions: Expanding allows us to write the expression in standard form, making it easier to graph the corresponding function.
- Simplifying expressions: Expanding can be used to simplify more complex expressions by combining like terms.
Understanding how to expand expressions like this is a crucial step in developing your algebraic skills.