(x+5)(x^2-6x+3)

Jasonbradley

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Jun 17, 2024

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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

1. Identify the terms: We have two sets of parentheses: (x + 5) and (x² - 6x + 3).
2. 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)
3. Distribute: Multiply each term individually.
   • x³ - 6x² + 3x + 5x² - 30x + 15
4. 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.