展开 (1+cos^2(7x))^3

解答

展开

(1 + cos^{2} (7 x))^{3}

1 + 3 cos^{2} (7 x) + 3 cos^{4} (7 x) + cos^{6} (7 x)

求解步骤

(1 + cos^{2} (7 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 + cos^{2} (7 x))^{3} = 1^{3} + 3 \cdot 1^{2} cos^{2} (7 x) + 3 \cdot 1 \cdot (cos^{2} (7 x))^{2} + (cos^{2} (7 x))^{3}

= 1^{3} + 3 \cdot 1^{2} cos^{2} (7 x) + 3 \cdot 1 \cdot (cos^{2} (7 x))^{2} + (cos^{2} (7 x))^{3}

化简

1^{3} + 3 \cdot 1^{2} cos^{2} (7 x) + 3 \cdot 1 \cdot (cos^{2} (7 x))^{2} + (cos^{2} (7 x))^{3} : 1 + 3 cos^{2} (7 x) + 3 cos^{4} (7 x) + cos^{6} (7 x)

= 1 + 3 cos^{2} (7 x) + 3 cos^{4} (7 x) + cos^{6} (7 x)

e x p an d \frac{- 6 s ^{2} + 12 s - 117}{( s - 2 ) ( - s ^{3} - 9 s )}

e x p an d ((sin (t))^{2} - 2 (e^{t})) (e^{t})

e x p an d \frac{1}{2 x ^{2} ( x - 2 ) ( 2 x + 1 ) ^{4} ( x ^{2} - 6 x + 10 )}

s im pl i f y (x - 37) (x + 37)

\frac{d}{d y} ((f (y)) (y + cos (y)))