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

Jasonbradley

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Jun 16, 2024

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Expanding the Expression: (x + 2)(x² - 2x + 1)

This expression represents the product of a binomial and a trinomial. To simplify it, we'll use the distributive property (also known as FOIL).

The Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend by that number and then adding the products.

In our case, we need to distribute each term of the binomial (x + 2) to each term of the trinomial (x² - 2x + 1).

Expanding the Expression

1. Multiply x by each term in the trinomial:

   • x * x² = x³
   • x * -2x = -2x²
   • x * 1 = x

2. Multiply 2 by each term in the trinomial:

   • 2 * x² = 2x²
   • 2 * -2x = -4x
   • 2 * 1 = 2

3. Combine the results:

   • x³ - 2x² + x + 2x² - 4x + 2

4. Simplify by combining like terms:

   • x³ - 3x + 2

Conclusion

Therefore, the expanded form of (x + 2)(x² - 2x + 1) is x³ - 3x + 2.