展开 (cosh(x)+sinh(x))^3

解答

展开

(cosh (x) + sinh (x))^{3}

cosh^{3} (x) + 3 cosh^{2} (x) sinh (x) + 3 sinh^{2} (x) cosh (x) + sinh^{3} (x)

求解步骤

(cosh (x) + sinh (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}

(cosh (x) + sinh (x))^{3} = cosh^{3} (x) + 3 cosh^{2} (x) sinh (x) + 3 cosh (x) sinh^{2} (x) + sinh^{3} (x)

= cosh^{3} (x) + 3 cosh^{2} (x) sinh (x) + 3 cosh (x) sinh^{2} (x) + sinh^{3} (x)

= cosh^{3} (x) + 3 cosh^{2} (x) sinh (x) + 3 sinh^{2} (x) cosh (x) + sinh^{3} (x)

e x p an d (u - 5) (u + 4 + 3)

e x p an d \frac{100}{( x ^{2} + 4 ) ( s ^{2} + 3 s + 5 )}

e x p an d \frac{Q ( a - b )}{4 π ( c - a ) ( b - c ) EF}

e x p an d \frac{x ^{2} + 3 x y}{y ( x + y )}

e x p an d \frac{z}{( z - j ^{2} ) ( z + j ^{2} )}