Form the equation whose roots are
$a + b, a - b, - a + b, - a - b$ .

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Solution

The equation whose roots are $a + b, a - b, b - a, - a - b$ is
${x - (a + b)} {x - (a - b)} {x - (- a + b)} {x - (- a - b)} = 0 {x - (a + b)} {x + (a + b)} {x - (a - b)} {x + (a - b)} = 0 {{x}^{2} - {(a + b)}^{2}} {x^{2} - {(a - b)}^{2}} = 0 x^{4} - {(a - b)}^{2} x^{2} - {(a + b)}^{2} x^{2} - {(a + b)}^{2} {(a - b)}^{2} = 0 x^{4} - {{(a - b)}^{2} - {(a + b)}^{2}} x^{2} - {(a + b)}^{2} {(a - b)}^{2} = 0 x^{4} + 4 a b x^{2} - {(a + b)}^{2} {(a - b)}^{2} = 0$

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