化简 (x-2i)^2

解答

化简

(x - 2 i)^{2}

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

求解步骤

(x - 2 i)^{2}

使用完全平方公式:

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

(x - 2 i)^{2} = x^{2} - 2 x \cdot 2 i + (2 i)^{2}

= x^{2} - 2 x \cdot 2 i + (2 i)^{2}

- 2 x \cdot 2 i = - 4 x i

(2 i)^{2} = - 4

= x^{2} - 4 x i - 4

Rewrite in standard complex form:

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

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

s im pl i f y (x - 1) (x + 1)

e x p an d (sin (x) + x cos (x))^{2}

e x p an d \frac{d ^{2}}{d x ^{2}} (x^{4}) - 2 x (6 x - x^{2})

e x p an d \frac{6 x ^{2} - 9 x + 1}{( x - 1 ) ^{2} ( x + 1 )}

s im pl i f y (x - 5) (x + 5)