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Expanding the Expression (3x-2)(x+4)
In mathematics, expanding an expression means simplifying it by removing parentheses. We can do this by applying the distributive property.
The Distributive Property:
The distributive property states that a(b + c) = ab + ac. We can use this property to expand the expression (3x-2)(x+4).
Steps:
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Multiply the first term of the first binomial by each term of the second binomial:
- 3x * x = 3x²
- 3x * 4 = 12x
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Multiply the second term of the first binomial by each term of the second binomial:
- -2 * x = -2x
- -2 * 4 = -8
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Combine all the terms:
- 3x² + 12x - 2x - 8
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Simplify by combining like terms:
- 3x² + 10x - 8
Therefore, the expanded form of (3x-2)(x+4) is 3x² + 10x - 8.
Applications:
Expanding expressions is a fundamental skill in algebra and is used in many different applications, including:
- Solving equations: Expanding expressions can help to simplify equations and make them easier to solve.
- Factoring expressions: Expanding expressions can help to identify factors of an expression.
- Graphing functions: Expanding expressions can help to determine the shape and location of the graph of a function.
Conclusion:
Expanding expressions like (3x-2)(x+4) is a key step in simplifying algebraic expressions and is crucial for many areas of mathematics. By understanding the distributive property, we can easily expand and simplify these expressions.