展开 (xcos(θ)+y)^2-x^2sin^2(θ)

解答

展开

(x cos (θ) + y)^{2} - x^{2} sin^{2} (θ)

x^{2} cos^{2} (θ) + 2 x y cos (θ) + y^{2} - x^{2} sin^{2} (θ)

求解步骤

(x cos (θ) + y)^{2} - x^{2} sin^{2} (θ)

使用完全平方公式:

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

(x cos (θ) + y)^{2} = (x cos (θ))^{2} + 2 x cos (θ) y + y^{2}

= (x cos (θ))^{2} + 2 x cos (θ) y + y^{2} - x^{2} sin^{2} (θ)

化简

(x cos (θ))^{2} + 2 x cos (θ) y + y^{2} : x^{2} cos^{2} (θ) + 2 x y cos (θ) + y^{2}

= x^{2} cos^{2} (θ) + 2 x y cos (θ) + y^{2} - x^{2} sin^{2} (θ)

\frac{\partial}{\partial x} ((y) (2 x - 3 y)^{3})

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

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

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

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