simplify : (q² - p²)(q² + p²) - ( q² + p²)
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(q² - p²)(q² + p²) - ( q² + p²)
use formula (a+b) (a-b) = a² - b²
= (q²)² - (p²)² - (q²+p²)
= q⁴ - p⁴ - (q²+p²)
= q⁴ - p⁴- q²- p²
= q⁴ - q² - p⁴ -p²
= (q²)² - (q)² - (p²)² - (p)²
use formula a²-b² = (a+b) (a-b)
= (q²+q) (q²-q) - (p²+p) (p²-p)
use formula (a+b) (a-b) = a² - b²
= (q²)² - (p²)² - (q²+p²)
= q⁴ - p⁴ - (q²+p²)
= q⁴ - p⁴- q²- p²
= q⁴ - q² - p⁴ -p²
= (q²)² - (q)² - (p²)² - (p)²
use formula a²-b² = (a+b) (a-b)
= (q²+q) (q²-q) - (p²+p) (p²-p)
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