化简 (x^2+2i)^2(x+4)

解答

化简

(x^{2} + 2 i)^{2} (x + 4)

(x^{5} + 4 x^{4} - 4 x - 16) + (4 x^{3} + 16 x^{2}) i

求解步骤

(x^{2} + 2 i)^{2} (x + 4)

展开

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

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

打开括号

= x^{4} x + x^{4} \cdot 4 + 4 x^{2} i x + 4 x^{2} i 4 - 4 x - 4 \cdot 4

化简

x^{4} x + x^{4} \cdot 4 + 4 x^{2} i x + 4 x^{2} i 4 - 4 x - 4 \cdot 4 : x^{5} + 4 x^{4} + 4 x^{3} i + 16 x^{2} i - 4 x - 16

= x^{5} + 4 x^{4} + 4 x^{3} i + 16 x^{2} i - 4 x - 16

Rewrite in standard complex form:

(x^{5} + 4 x^{4} - 4 x - 16) + (4 x^{3} + 16 x^{2}) i

= (x^{5} + 4 x^{4} - 4 x - 16) + (4 x^{3} + 16 x^{2}) i

e x p an d sec (a) (1 - sin (a)) (sec (a) + tan (a))

e x p an d (x - 2)^{2} (x - (6 i)) (x - (- 6 i))

e x p an d x^{2 (a - 2)} - y^{6 b}

e x p an d 2 (e^{\frac{π}{2}} - 1)

s im pl i f y (x - 1) \times x