Question

Prove that the value of the expression does not depend on the variable x: x4–(x2–1)(x2+1)

Answer 1

$x^4 - (x^2-1)(x^2+1) = x^4 - (x^4-1) =x^4 - x^4 + 1= \boxed{1}$

The expression does not depend on the variable x as your final answer will always be 1.

Answer 2

$x^4 - (x^2-1)(x^2+1)$

Use the formula: (a+b)(a-b) = a^2 - b^2

$x^4 - [(x^2)^2 - 1^2]\\\\x^4 - (x^4-1)\\\\x^4 - x^4 + 1\\\\\boxed{\bf{1}}$

No matter what the value of 'x' is, the final answer will always be 1.