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

Jasonbradley

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Jun 16, 2024

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Solving the Equation: (x+2)(x^2-2x+4)-(x-2)(x^2+2x+4)=4x

This article will explore how to solve the equation (x+2)(x^2-2x+4)-(x-2)(x^2+2x+4)=4x. We will utilize algebraic manipulation and factorization to find the solution(s) for x.

Expanding the Equation

First, we need to expand the equation by multiplying out the terms:

• (x+2)(x^2-2x+4): Using the distributive property (or FOIL method), we get: x³ - 2x² + 4x + 2x² - 4x + 8 = x³ + 8
• (x-2)(x² + 2x + 4): Similarly, this gives us: x³ + 2x² + 4x - 2x² - 4x - 8 = x³ - 8

Now, the equation becomes: x³ + 8 - (x³ - 8) = 4x

Simplifying the Equation

Combining like terms, we get:

• x³ - x³ + 8 + 8 = 4x
• 16 = 4x

Solving for x

Finally, we isolate x by dividing both sides by 4:

• x = 16 / 4
• x = 4

Therefore, the solution to the equation (x+2)(x^2-2x+4)-(x-2)(x^2+2x+4)=4x is x = 4.