(4x^2-4x-4) (x+4)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (4x² - 4x - 4)(x + 4)

This article will guide you through the process of expanding the expression (4x² - 4x - 4)(x + 4). We'll use the distributive property (also known as FOIL) 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 by the number and then adding the results. In our case, we'll be multiplying each term in the first polynomial (4x² - 4x - 4) by each term in the second polynomial (x + 4).

Expanding the Expression

1. Multiply the first term of the first polynomial (4x²) by each term in the second polynomial:

   • 4x² * x = 4x³
   • 4x² * 4 = 16x²

2. Multiply the second term of the first polynomial (-4x) by each term in the second polynomial:

   • -4x * x = -4x²
   • -4x * 4 = -16x

3. Multiply the third term of the first polynomial (-4) by each term in the second polynomial:

   • -4 * x = -4x
   • -4 * 4 = -16

4. Combine all the terms:

   • 4x³ + 16x² - 4x² - 16x - 4x - 16

5. Simplify by combining like terms:

   • 4x³ + 12x² - 20x - 16

Final Result

Therefore, the expanded form of (4x² - 4x - 4)(x + 4) is 4x³ + 12x² - 20x - 16.