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

Jasonbradley

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Jun 16, 2024

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Factoring and Expanding (x+2)(x+1)(x-1)

This article will explore the process of factoring and expanding the expression (x+2)(x+1)(x-1).

Factoring the Expression

The expression is already factored, as it is presented as a product of three binomials: (x+2), (x+1), and (x-1). However, we can further simplify it by expanding the product.

Expanding the Expression

To expand the expression, we can use the distributive property or the FOIL method.

Step 1: Expand the first two binomials

(x+2)(x+1) = x(x+1) + 2(x+1)

         = x² + x + 2x + 2

         = x² + 3x + 2

Step 2: Multiply the result by the third binomial

(x² + 3x + 2)(x-1) = x²(x-1) + 3x(x-1) + 2(x-1)

               = x³ - x² + 3x² - 3x + 2x - 2

               = **x³ + 2x² - x - 2**

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

Key Points

• The distributive property allows us to multiply each term in one binomial by every term in the other.
• FOIL (First, Outer, Inner, Last) is a mnemonic for remembering the order of multiplications when expanding two binomials.
• Expanding a factored expression allows us to express it as a single polynomial.

This exploration demonstrates how to factor and expand the expression (x+2)(x+1)(x-1), providing a comprehensive understanding of the process.