化简 (x+4i)^3(x-4i)

解答

化简

(x + 4 i)^{3} (x - 4 i)

(x^{4} - 256) + (8 x^{3} + 128 x) i

求解步骤

(x + 4 i)^{3} (x - 4 i)

展开

(x + 4 i)^{3} : x^{3} + 12 x^{2} i - 48 x - 64 i

= (x^{3} + 12 x^{2} i - 48 x - 64 i) (x - 4 i)

打开括号

= x^{3} x + x^{3} (- 4 i) + 12 x^{2} i x + 12 x^{2} i (- 4 i) - 48 xx - 48 x (- 4 i) - 64 i x - 64 i (- 4 i)

化简

x^{3} x + x^{3} (- 4 i) + 12 x^{2} i x + 12 x^{2} i (- 4 i) - 48 xx - 48 x (- 4 i) - 64 i x - 64 i (- 4 i) : x^{4} + 8 x^{3} i + 128 x i - 256

= x^{4} + 8 x^{3} i + 128 x i - 256

Rewrite in standard complex form:

(x^{4} - 256) + (8 x^{3} + 128 x) i

= (x^{4} - 256) + (8 x^{3} + 128 x) i

e x p an d \frac{cos ( x ) ( 1 - x ^{2} ) + 2 x sin ( x )}{( 1 - x ^{2} ) ^{2}}

e x p an d f (x) ((x) = \frac{4}{7} x - \frac{16}{7})

e x p an d (9 - x) (\frac{2}{3} x + 4)

s im pl i f y (x - 11 - 3) (x - 2) (x - 4) (x - 11 + 3)

e x p an d (2, - 2) (2 x, 3) (4, 3)