Question

(x^4 - 4x^3 + 16x - 16) (x^4 - 4x^3 + 8x^2 - 16x + 16)

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Answer 1

   Х⁴ - 4 * Х³ + 16 * Х - 16             (Х⁴ - 4 * Х³ + 4 * Х²) - (4 * Х² - 16 * Х + 16)

-------------------------------------- = ------------------------------------------------------ =

Х⁴ - 4 * Х³ + 8 * Х² -16 * Х + 16      (Х⁴ - 4 * Х³ + 4 * Х²) + (4 * Х² - 16 * Х + 16)

(Х² - 2 * Х)² - (2 * Х - 4)²     (Х - 2)² * (Х² - 4)        Х² - 4

------------------------------ = ----------------------- = -----------

(Х² - 2 * Х)² + (2 * Х - 4)²     (Х - 2)² * (Х² + 4)       Х² + 4

Answer 2

$frac{x^4-4x^3+16x-16}{x^4-4x^3+8x^2-16x+16}=frac{(x^2-4)(x^2+4)-4x(x^2-4)}{(x^2+4)^2-4x(x^2+4)}=$

= $frac{(x^2-4)(x^2-4x+4)}{(x^2+4)(x^2-4x+4)} = frac{x^2-4}{x^2+4}.$