x^2+4abx-(a^2-b^2)^2

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Solution

x² - 4abx - (a2 - b2)²
= x² - 4abx + 4a²b²- 4a²b² - (a² - b²)²
= (x)² - 2x2ab + (2ab)² - 4a²b² - (a⁴ + b⁴ - 2a²b²)
= (x - 2ab)² - 4a²b² - a⁴ - b⁴ + 2a²b²
= (x - 2ab)² - a⁴ - b⁴ - 2a²b²
= (x - 2ab)² - (a⁴ + b⁴ + 2a²b²)
= (x - 2ab)² - [(a²)² + (b²)² + 2a²b²]
= (x - 2ab)² - (a² + b²)²
= [(x - 2ab) + (a² + b²)] * [(x - 2ab) - (a² + b²)]
= [x - 2ab + a² + b²] * [x - 2ab - a² + b²]
= [x + a² + b² - 2ab] * [x - (a² + b² + 2ab]
= [x + (a - b)²] * [x - (a + b)²]

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