急~因式分解： x（x-1)(x-2)-6            和 a⁸+a⁴b⁴+b⁸?

x(x - 1)(x - 2) - 6
= x(x² - 3x + 2) - 6
= x³ - 3x² + 2x - 6
= (x³ - 3x²) + (2x - 6)
= x²(x - 3) + 2(x - 3)
= (x - 3)(x² + 2)

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a⁸ + a⁴b⁴ + b⁸
= (a⁸ + 2a⁴b⁴ + b⁸) - a⁴b⁴
= [(a⁴)² + 2a⁴b⁴ + (b⁴)²] - (a²b²)²
= (a⁴ + b⁴)² - (a²b²)²
= [(a⁴ + b⁴) - a²b²] [(a⁴ + b⁴) + a²b²]
= (a⁴ - a²b² + b⁴) [(a⁴ + 2a²b² + b⁴) - a²b²]
= (a⁴ - a²b² + b⁴) {[(a²)² + 2a²b² + (b²)²] - a²b²}
= (a⁴ - a²b² + b⁴) [(a² + b²)² - (ab)²]
= (a⁴ - a²b² + b⁴) [(a² + b²) + (ab)] [(a² + b²) + (ab)]
= (a⁴ - a²b² + b⁴)(a² + ab + b²)(a² - ab + b²)

x(x-1)(x-2)-6 = x^3-3x^2+2x-6 
    = x^2(x-3) + 2(x-3)
    = (x^2+2)(x-3)

a^8 + a^4b^4 + b^8 = (a^12-b^12)/(a^4-b^4)
   = [(a^6-b^6)(a^6+b^6)]/[(a^2-b^2)(a^2+b^2)]
   = [(a^3-b^3)(a^3+b^3)(a^6+b^6)]/[(a-b)(a+b)(a^2+b^2)]
   = (a^3-b^3)/(a-b) (a^3+b^3)/(a+b) (a^6+b^6)/(a^2+b^2)
   = (a^2+ab+b^2)(a^2-ab+b^2)(a4-a^2b^2+b^4)