(x-2)(x^2-5x+1)-x(x^2+11)

Jasonbradley

2 min read

·

Jun 17, 2024

25

Share

Simplifying the Expression (x-2)(x^2-5x+1)-x(x^2+11)

This article will guide you through the steps involved in simplifying the algebraic expression: (x-2)(x^2-5x+1)-x(x^2+11).

Expanding the Expression

The first step is to expand the expression by using the distributive property.

• Expand (x-2)(x^2-5x+1):

  • Multiply each term in the first set of parentheses by each term in the second set:
  • x(x^2-5x+1) - 2(x^2-5x+1) = x^3 - 5x^2 + x - 2x^2 + 10x - 2

• Expand -x(x^2+11):

  • -x(x^2+11) = -x^3 - 11x

Combining Like Terms

Now, we combine like terms:

• Combine x^3 terms: x^3 - x^3 = 0
• Combine x^2 terms: -5x^2 - 2x^2 = -7x^2
• Combine x terms: x + 10x - 11x = 0
• Combine constant terms: -2

Simplified Expression

The simplified form of the expression is:

-7x^2 - 2