展开 3(x-y)^2(1-(dy)/(dx))

解答

展开

3 (x - y)^{2} (1 - \frac{d y}{d x})

3 x^{2} - 6 x y + 3 y^{2} - 3 x^{2} \frac{d y}{d x} + 6 x y \frac{d y}{d x} - 3 y^{2} \frac{d y}{d x}

求解步骤

3 (x - y)^{2} (1 - \frac{d y}{d x})

使用分配律:

a (b - c) = ab - a c

a = 3 (x - y)^{2}, b = 1, c = \frac{d y}{d x}

= 3 (x - y)^{2} \cdot 1 - 3 (x - y)^{2} \frac{d y}{d x}

= 3 \cdot 1 \cdot (x - y)^{2} - 3 (x - y)^{2} \frac{d y}{d x}

化简

3 \cdot 1 \cdot (x - y)^{2} - 3 (x - y)^{2} \frac{d y}{d x} : 3 x^{2} - 6 x y + 3 y^{2} - 3 x^{2} \frac{d y}{d x} + 6 x y \frac{d y}{d x} - 3 y^{2} \frac{d y}{d x}

= 3 x^{2} - 6 x y + 3 y^{2} - 3 x^{2} \frac{d y}{d x} + 6 x y \frac{d y}{d x} - 3 y^{2} \frac{d y}{d x}

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