(x-2)(x^2+8x-1)

Jasonbradley

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Jun 17, 2024

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Expanding and Simplifying the Expression (x-2)(x^2+8x-1)

This expression involves multiplying a binomial (x-2) with a trinomial (x^2+8x-1). We can achieve this by using the distributive property, also known as FOIL (First, Outer, Inner, Last).

Applying the Distributive Property

1. First: Multiply the first terms of each expression: (x) * (x^2) = x^3
2. Outer: Multiply the outer terms of each expression: (x) * (-1) = -x
3. Inner: Multiply the inner terms of each expression: (-2) * (x^2) = -2x^2
4. Last: Multiply the last terms of each expression: (-2) * (-1) = 2

Now, combine all the terms:

x^3 - x - 2x^2 + 2

Simplifying the Expression

Finally, we can combine like terms to get the simplified form:

x^3 - 2x^2 - x + 2

Therefore, the expanded and simplified form of the expression (x-2)(x^2+8x-1) is x^3 - 2x^2 - x + 2.