(x-3)(x^2+2x+1)

Jasonbradley

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Jun 17, 2024

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Expanding the Expression: (x-3)(x^2+2x+1)

This article will walk through the process of expanding the given expression, (x-3)(x^2+2x+1). We will utilize the distributive property and simplify the result.

Understanding the Problem

The expression is a product of two factors:

• (x-3): This is a binomial, meaning it contains two terms.
• (x^2+2x+1): This is a trinomial, containing three terms.

The Distributive Property

To expand the expression, we can use the distributive property, which states that:

a(b + c) = ab + ac

This means we need to multiply each term in the first factor by each term in the second factor.

Expanding the Expression

Let's apply the distributive property step by step:

1. Multiply (x-3) by x^2: (x-3) * x^2 = xx^2 - 3x^2 = x^3 - 3x^2

2. Multiply (x-3) by 2x: (x-3) * 2x = x2x - 32x = 2x^2 - 6x

3. Multiply (x-3) by 1: (x-3) * 1 = x1 - 31 = x - 3

4. Combine all terms: x^3 - 3x^2 + 2x^2 - 6x + x - 3 = x^3 - x^2 - 5x - 3

Final Result

Therefore, the expanded form of (x-3)(x^2+2x+1) is x^3 - x^2 - 5x - 3.