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Expanding the Expression (x + 5)(x² - 6x + 3)
This article will guide you through the process of expanding the expression (x + 5)(x² - 6x + 3) using the distributive property.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. In mathematical terms:
- a(b + c) = ab + ac
Expanding the Expression
- Identify the terms: We have two sets of parentheses: (x + 5) and (x² - 6x + 3).
- Apply the distributive property: We will multiply each term in the first set of parentheses by each term in the second set of parentheses.
- x(x² - 6x + 3) + 5(x² - 6x + 3)
- Distribute: Multiply each term individually.
- x³ - 6x² + 3x + 5x² - 30x + 15
- Combine like terms: Combine the terms with the same variable and exponent.
- x³ - x² - 27x + 15
Final Result
Therefore, the expanded form of (x + 5)(x² - 6x + 3) is x³ - x² - 27x + 15.
Additional Notes
- This process is known as polynomial multiplication.
- The expanded expression is a cubic polynomial because the highest power of the variable is 3.
- You can use this method to expand any expression with multiple sets of parentheses.