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Expanding the Expression (x+3)(x^2-2x+5)
This article will guide you through the process of expanding the expression (x+3)(x^2-2x+5). This is a common algebraic manipulation that involves the distributive property.
Understanding the Distributive Property
The distributive property states that for any numbers a, b, and c:
a(b+c) = ab + ac
This means that we can multiply a term by a sum of terms by multiplying the term with each individual term inside the sum.
Applying the Distributive Property
Let's apply the distributive property to our expression:
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Multiply (x+3) by the first term in the second parenthesis, x²:
(x+3)(x²-2x+5) = x(x²-2x+5) + 3(x²-2x+5)
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Distribute x and 3 to each term inside the parentheses:
x(x²-2x+5) + 3(x²-2x+5) = x³ - 2x² + 5x + 3x² - 6x + 15
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Combine like terms:
x³ - 2x² + 5x + 3x² - 6x + 15 = x³ + x² - x + 15
Final Result
Therefore, the expanded form of the expression (x+3)(x²-2x+5) is x³ + x² - x + 15.
Key Takeaways
- Understanding the distributive property is crucial for expanding algebraic expressions.
- Remember to distribute each term outside the parentheses to each term inside the parentheses.
- Combine like terms after distribution to simplify the expression.