展开 (x-2)(x-3)(x-1+i)

解答

展开

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

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

求解步骤

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

展开

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

= (x^{2} - 5 x + 6) (x - 1 + i)

打开括号

= x^{2} x + x^{2} (- 1) + x^{2} i - 5 xx - 5 x (- 1) - 5 x i + 6 x + 6 (- 1) + 6 i

化简

x^{2} x + x^{2} (- 1) + x^{2} i - 5 xx - 5 x (- 1) - 5 x i + 6 x + 6 (- 1) + 6 i : 6 i + x^{3} - 6 x^{2} + x^{2} i + 11 x - 5 x i - 6

= 6 i + x^{3} - 6 x^{2} + x^{2} i + 11 x - 5 x i - 6

Rewrite in standard complex form:

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

= (x^{3} - 6 x^{2} + 11 x - 6) + (6 + x^{2} - 5 x) i

e x p an d co v (α X + b, c Y + d)

e x p an d (z - 0) (z - 5) (z - (1 - 5))

e x p an d (x^{\frac{1}{2}})^{2}

s im pl i f y 2 u^{2} + 2 v^{2} + 4 ((u^{2} + v^{2}))

e x p an d (2 m - 3 b) e^{3}