展开 \sqrt[4]{(x-1)}(x+1)(x^2+1)(x^4+1)+1

解答

展开

4 (x - 1) (x + 1) (x^{2} + 1) (x^{4} + 1) + 1

x^{7} 4 x - 1 + x^{5} 4 x - 1 + x^{6} 4 x - 1 + x^{4} 4 x - 1 + x^{3} 4 x - 1 + x 4 x - 1 + x^{2} 4 x - 1 + 4 x - 1 + 1

求解步骤

4 x - 1 (x + 1) (x^{2} + 1) (x^{4} + 1) + 1

化简

(x - 1) : x - 1

= 4 x - 1 (x + 1) (x^{2} + 1) (x^{4} + 1) + 1

展开

4 x - 1 (x + 1) (x^{2} + 1) (x^{4} + 1) : x^{7} 4 x - 1 + x^{5} 4 x - 1 + x^{6} 4 x - 1 + x^{4} 4 x - 1 + x^{3} 4 x - 1 + x 4 x - 1 + x^{2} 4 x - 1 + 4 x - 1

= x^{7} 4 x - 1 + x^{5} 4 x - 1 + x^{6} 4 x - 1 + x^{4} 4 x - 1 + x^{3} 4 x - 1 + x 4 x - 1 + x^{2} 4 x - 1 + 4 x - 1 + 1

s im pl i f y (a - b 2) (a + b 2)

e x p an d (\frac{t ^{2}}{8} - \frac{t ^{3}}{12})^{2}

e x p an d - (1 + 7 x) - 6 (- 7 - x = 36)

e x p an d lo g_{10} (2) (\frac{2 x + 1}{x - 5})

e x p an d 2 (x^{2} - 7 x + 7)^{2}