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(x+1)(x+1)-(x-1)(x-1)=4

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

Solving the Equation (x+1)(x+1) - (x-1)(x-1) = 4

This equation involves simplifying and solving for the unknown variable 'x'. Let's break down the steps:

1. Expanding the Equation

First, we need to expand the expressions on both sides of the equation:

  • (x+1)(x+1) can be expanded using the FOIL method (First, Outer, Inner, Last):
    • x * x + x * 1 + 1 * x + 1 * 1 = x² + 2x + 1
  • (x-1)(x-1) can also be expanded using the FOIL method:
    • x * x + x * -1 + -1 * x + -1 * -1 = x² - 2x + 1

Now our equation looks like this: x² + 2x + 1 - (x² - 2x + 1) = 4

2. Simplifying the Equation

Next, we can simplify the equation by removing the parentheses and combining like terms:

  • x² + 2x + 1 - x² + 2x - 1 = 4
  • 4x = 4

3. Solving for 'x'

Finally, we can solve for 'x' by dividing both sides of the equation by 4:

  • x = 1

Solution

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

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