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

2 min read Jun 17, 2024
(x+5)(x^2-6x+3)

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.