Question

(x-1)(x+1)+(x+1)(x-5)-(x-5)(x+5)

Answer 1

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Answer 2

To simplify the expression (x-1)(x+1) + (x+1)(x-5) - (x-5)(x+5), you can use the distributive property (FOIL) to expand each term and then combine like terms:

1. Expand each term:

   • (x-1)(x+1) = x^2 - 1
   • (x+1)(x-5) = x^2 - 5x + x - 5 = x^2 - 4x - 5
   • (x-5)(x+5) = x^2 + 5x - 5x - 25 = x^2 - 25

2. Now, substitute these expanded forms back into the original expression and combine like terms:

   (x^2 - 1) + (x^2 - 4x - 5) - (x^2 - 25)

3. Combine like terms within parentheses:

   x^2 + x^2 - 4x - 1 - 5 - x^2 + 25

4. Combine like terms again:

   (x^2 + x^2 - x^2) + (-4x - 1 - 5 + 25)

5. Simplify:

   x^2 - 4x + 19

So, the simplified expression is x^2 - 4x + 19.