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

Jasonbradley

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Jun 16, 2024

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

This article will guide you through the process of expanding the expression (2x^2 - x + 1)(x - 3). We will use the distributive property, also known as FOIL (First, Outer, Inner, Last), to achieve this.

Understanding the Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the products together. In simpler terms, we distribute the number outside the parentheses to each term inside the parentheses.

Expanding the Expression

1. Multiply the first term of the first factor by each term in the second factor.

   • (2x^2)(x) = 2x^3
   • (2x^2)(-3) = -6x^2

2. Multiply the second term of the first factor by each term in the second factor.

   • (-x)(x) = -x^2
   • (-x)(-3) = 3x

3. Multiply the third term of the first factor by each term in the second factor.

   • (1)(x) = x
   • (1)(-3) = -3

4. Combine all the terms.

   • 2x^3 - 6x^2 - x^2 + 3x + x - 3

5. Simplify by combining like terms.

   • 2x^3 - 7x^2 + 4x - 3

Final Result

Therefore, the expanded form of (2x^2 - x + 1)(x - 3) is 2x^3 - 7x^2 + 4x - 3.