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受欢迎的代数 >

化简 (x-3)(x-2-i)(x+2+i)

解答

化简

(x - 3) (x - 2 - i) (x + 2 + i)

解答

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

求解步骤

(x - 3) (x - 2 - i) (x + 2 + i)

将

x - 2 - i

改写成标准复数形式:

(x - 2) - i

= (x - 3) ((x - 2) - i) (x + 2 + i)

使用复数算数法则:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

= (x - 3) (((x - 2) (x + 2) - (- 1) \cdot 1) + ((x - 2) \cdot 1 - 1 \cdot (x + 2)) i)

化简

((x - 2) (x + 2) - (- 1) \cdot 1) + ((x - 2) \cdot 1 - 1 \cdot (x + 2)) i : (x^{2} - 3) - 4 i

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

打开括号

= (x - 3) (x^{2} - 3) - (x - 3) \cdot 4 i

展开

- (x - 3) \cdot 4 : - 4 x + 12

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

流行的例子

展开 (ln(x))^{sec(x)}

e x p an d (ln (x))^{s e c (x)}

展开 (3-cos(x))^2

e x p an d (3 - cos (x))^{2}

化简 (sqrt(x-3)+1)^2

s im pl i f y (x - 3 + 1)^{2}

展开 ((4x+9)^{3/2}-27)/6

e x p an d \frac{( 4 x + 9 ) ^{\frac{3}{2}} - 27}{6}

展开 (36x)/((9-x^2)^2)

e x p an d \frac{36 x}{( 9 - x ^{2} ) ^{2}}