(x%5E2-5x%2B1)-x(x%5E2%2B11).jpeg "(x-2)(x^2-5x+1)-x(x^2+11)")
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.
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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
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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