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

Jasonbradley

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Jun 17, 2024

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Expanding the Expression: (x-2)(x^2+x-1)

This expression represents the product of two polynomials: a binomial (x-2) and a trinomial (x^2+x-1). To expand it, we can use the distributive property (often referred to as FOIL for binomials).

Step-by-step Expansion:

1. Distribute the 'x' from the first binomial:

   • x * (x^2+x-1) = x^3 + x^2 - x

2. Distribute the '-2' from the first binomial:

   • -2 * (x^2+x-1) = -2x^2 - 2x + 2

3. Combine the results from steps 1 and 2:

   • x^3 + x^2 - x - 2x^2 - 2x + 2

4. Simplify by combining like terms:

   • x^3 - x^2 - 3x + 2

Final Result:

Therefore, the expanded form of (x-2)(x^2+x-1) is x^3 - x^2 - 3x + 2.

Applications and Considerations:

Expanding expressions like this is crucial in various mathematical contexts, including:

• Solving equations: Expanding the expression might be necessary to simplify an equation before applying other solving techniques.
• Finding roots: The expanded form can be used to find the roots (solutions) of the polynomial equation.
• Graphing functions: Understanding the expanded form helps in visualizing the behavior of the function represented by the expression.

Remember that expanding expressions allows for further manipulation and analysis, revealing valuable insights and making calculations easier.