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

Multiply x by each term in the trinomial:
 x * x² = x³
 x * 2x = 2x²
 x * 1 = x

Multiply 2 by each term in the trinomial:
 2 * x² = 2x²
 2 * 2x = 4x
 2 * 1 = 2

Combine the results:
 x³  2x² + x + 2x²  4x + 2

Simplify by combining like terms:
 x³  3x + 2
Conclusion
Therefore, the expanded form of (x + 2)(x²  2x + 1) is x³  3x + 2.