化简 (t-it^2)^2

解答

化简

(t - i t^{2})^{2}

(t^{2} - t^{4}) - 2 t^{3} i

求解步骤

(t - i t^{2})^{2}

使用完全平方公式:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(t - i t^{2})^{2} = t^{2} - 2 t i t^{2} + (i t^{2})^{2}

= t^{2} - 2 t i t^{2} + (i t^{2})^{2}

- 2 t i t^{2} = - 2 t^{3} i

(i t^{2})^{2} = - t^{4}

= t^{2} - 2 t^{3} i - t^{4}

Rewrite in standard complex form:

(t^{2} - t^{4}) - 2 t^{3} i

= (t^{2} - t^{4}) - 2 t^{3} i

e x p an d 5 (15 + 22 e^{\frac{4 l n ( \frac{15}{22} )}{3}})

e x p an d (y^{4} + 8 x y^{4} - x^{3}) d x + (4 x y^{3} + 16 x^{2} y^{3}) d y

s im pl i f y (y - \frac{1}{3}) (y - \frac{2}{3})

e x p an d \frac{5 ( 3 x ^{3} + 2 x ) ^{\frac{3}{2}} ( 9 x ^{2} + 2 )}{2}

e x p an d (2 x^{\frac{5}{3}} + 3) (16 x^{3} - 8 x)