展开 (x+2)(x-1)(x-(4+i))(x-(4-i))

解答

展开

(x + 2) (x - 1) (x - (4 + i)) (x - (4 - i))

x^{4} - 7 x^{3} + 7 x^{2} + 33 x - 34

求解步骤

(x + 2) (x - 1) (x - (4 + i)) (x - (4 - i))

展开

(x + 2) (x - 1) (x - (4 + i)) (x - (4 - i)) : (x^{2} + x - 2) (x - (4 + i)) (x - (4 - i))

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

Apply FOIL method

(x - (4 + i)) (x - (4 - i)) : x^{2} + 17 - 8 x

= (x^{2} + x - 2) (x^{2} + 17 - 8 x)

打开括号

= x^{2} x^{2} + x^{2} \cdot 17 + x^{2} (- 8 x) + x x^{2} + x \cdot 17 + x (- 8 x) - 2 x^{2} - 2 \cdot 17 - 2 (- 8 x)

化简

x^{2} x^{2} + x^{2} \cdot 17 + x^{2} (- 8 x) + x x^{2} + x \cdot 17 + x (- 8 x) - 2 x^{2} - 2 \cdot 17 - 2 (- 8 x) : x^{4} - 7 x^{3} + 7 x^{2} + 33 x - 34

= x^{4} - 7 x^{3} + 7 x^{2} + 33 x - 34

e x p an d (2 x + \frac{1}{x})^{4}

e x p an d (a, b) (b, - a)

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

e x p an d (x + y^{'} (x)) (x + y)

e x p an d (x + y i)^{5}