展开 (2x-1)(x-2)(x-3)(x-4-i)(x-4+i)

解答

展开

(2 x - 1) (x - 2) (x - 3) (x - 4 - i) (x - 4 + i)

2 x^{5} - 27 x^{4} + 139 x^{3} - 329 x^{2} + 337 x - 102

求解步骤

(2 x - 1) (x - 2) (x - 3) (x - 4 - i) (x - 4 + i)

展开

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

= (2 x^{2} - 5 x + 2) (x - 3) (x - 4 - i) (x - 4 + i)

展开

(2 x^{2} - 5 x + 2) (x - 3) : 2 x^{3} - 11 x^{2} + 17 x - 6

= (2 x^{3} - 11 x^{2} + 17 x - 6) (x - 4 - i) (x - 4 + i)

展开

(2 x^{3} - 11 x^{2} + 17 x - 6) (x - 4 - i) : 6 i + 2 x^{4} - 19 x^{3} - 2 x^{3} i + 61 x^{2} + 11 x^{2} i - 74 x - 17 x i + 24

= (6 i + 2 x^{4} - 19 x^{3} - 2 x^{3} i + 61 x^{2} + 11 x^{2} i - 74 x - 17 x i + 24) (x - 4 + i)

打开括号

= 6 i x + 6 i (- 4) + 6 ii + 2 x^{4} x + 2 x^{4} (- 4) + 2 x^{4} i - 19 x^{3} x - 19 x^{3} (- 4) - 19 x^{3} i - 2 x^{3} i x - 2 x^{3} i (- 4) - 2 x^{3} ii + 61 x^{2} x + 61 x^{2} (- 4) + 61 x^{2} i + 11 x^{2} i x + 11 x^{2} i (- 4) + 11 x^{2} ii - 74 xx - 74 x (- 4) - 74 x i - 17 x i x - 17 x i (- 4) - 17 x ii + 24 x + 24 (- 4) + 24 i

化简

6 i x + 6 i (- 4) + 6 ii + 2 x^{4} x + 2 x^{4} (- 4) + 2 x^{4} i - 19 x^{3} x - 19 x^{3} (- 4) - 19 x^{3} i - 2 x^{3} i x - 2 x^{3} i (- 4) - 2 x^{3} ii + 61 x^{2} x + 61 x^{2} (- 4) + 61 x^{2} i + 11 x^{2} i x + 11 x^{2} i (- 4) + 11 x^{2} ii - 74 xx - 74 x (- 4) - 74 x i - 17 x i x - 17 x i (- 4) - 17 x ii + 24 x + 24 (- 4) + 24 i : 2 x^{5} - 27 x^{4} + 139 x^{3} - 329 x^{2} + 337 x - 102

= 2 x^{5} - 27 x^{4} + 139 x^{3} - 329 x^{2} + 337 x - 102

s im pl i f y 4 x (5 x - 1)

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