展开 (1+tan(x))^3

解答

展开

(1 + tan (x))^{3}

1 + 3 tan (x) + 3 tan^{2} (x) + tan^{3} (x)

求解步骤

(1 + tan (x))^{3}

使用完全立方公式:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(1 + tan (x))^{3} = 1^{3} + 3 \cdot 1^{2} tan (x) + 3 \cdot 1 \cdot tan^{2} (x) + tan^{3} (x)

= 1^{3} + 3 \cdot 1^{2} tan (x) + 3 \cdot 1 \cdot tan^{2} (x) + tan^{3} (x)

化简

1^{3} + 3 \cdot 1^{2} tan (x) + 3 \cdot 1 \cdot tan^{2} (x) + tan^{3} (x) : 1 + 3 tan (x) + 3 tan^{2} (x) + tan^{3} (x)

= 1 + 3 tan (x) + 3 tan^{2} (x) + tan^{3} (x)

e x p an d \frac{( ( 3 s - 1 ) ( 2 s - 1 ) )}{( s ( s ^{2} - 2 s + 14 ) )}

e x p an d \frac{s - 1}{( s + 1 ) ( s + 2 ) ( s + 3 ) ( s + 4 )}

e x p an d \frac{7}{( x + 1 ) ^{2}}

e x p an d \frac{2 x ^{3} - 24 x ^{2} + 71 x - 63}{( x - 4 ) ^{2} ( x ^{2} - 3 x + 3 )}

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