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

Jasonbradley

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Jun 16, 2024

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

This article will guide you through the process of solving the algebraic equation:

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

Let's break down the steps to find the solution:

1. Expanding the Equation

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

• (x+1)(x^2+2x-1):
  • x * x^2 + x * 2x + x * -1 + 1 * x^2 + 1 * 2x + 1 * -1
  • x^3 + 2x^2 - x + x^2 + 2x - 1
  • x^3 + 3x^2 + x - 1
• -x^2(x+3):
  • -x^2 * x + -x^2 * 3
  • -x^3 - 3x^2

Now, our equation becomes:

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

2. Simplifying the Equation

Notice that the x^3 and 3x^2 terms cancel out:

x - 1 = 4

3. Solving for x

Finally, we isolate x:

• x = 4 + 1
• x = 5

Therefore, the solution to the equation (x+1)(x^2+2x-1)-x^2(x+3)=4 is x = 5.