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(x+1)(x^2-x+1)-x(x^2-3)=4

2 min read Jun 16, 2024
(x+1)(x^2-x+1)-x(x^2-3)=4

Solving the Equation (x+1)(x^2-x+1)-x(x^2-3)=4

This article will guide you through solving the equation (x+1)(x^2-x+1)-x(x^2-3)=4.

Expanding the Equation

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

  • (x+1)(x^2-x+1):
    • Use the distributive property (FOIL method) to multiply each term in the first parenthesis with each term in the second.
    • This results in: x^3 - x^2 + x + x^2 - x + 1 = x^3 + 1
  • -x(x^2-3):
    • Distribute the -x: -x^3 + 3x

Now the equation becomes: x^3 + 1 - x^3 + 3x = 4

Simplifying the Equation

Combining like terms, we get: 3x + 1 = 4

Isolating the Variable

To isolate x, subtract 1 from both sides of the equation: 3x = 3

Solving for x

Finally, divide both sides by 3 to get the solution: x = 1

Therefore, the solution to the equation (x+1)(x^2-x+1)-x(x^2-3)=4 is x = 1.

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