展开 (x-2)^2(x-(6i))(x-(-6i))

解答

展开

(x - 2)^{2} (x - (6 i)) (x - (- 6 i))

x^{4} - 4 x^{3} + 40 x^{2} - 144 x + 144

求解步骤

(x - 2)^{2} (x - (6 i)) (x - (- 6 i))

化简

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

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

Apply Difference of Two Squares

(x - 6 i) (x + 6 i) : x^{2} + 36

= (x - 2)^{2} (x^{2} + 36)

展开

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

= (x^{2} - 4 x + 4) (x^{2} + 36)

打开括号

= x^{2} x^{2} + x^{2} \cdot 36 - 4 x x^{2} - 4 x \cdot 36 + 4 x^{2} + 4 \cdot 36

化简

x^{2} x^{2} + x^{2} \cdot 36 - 4 x x^{2} - 4 x \cdot 36 + 4 x^{2} + 4 \cdot 36 : x^{4} - 4 x^{3} + 40 x^{2} - 144 x + 144

= x^{4} - 4 x^{3} + 40 x^{2} - 144 x + 144

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

e x p an d (4 x^{3} - \frac{3}{x ^{2}})^{5}

e x p an d lo g_{2} (32 x^{7})