展開する (5x+8((dy)/(dx)))^2

解

展開する

(5 x + 8 (\frac{d y}{d x}))^{2}

25 x^{2} + 80 x \frac{d y}{d x} + 64 \frac{d y}{d x}^{2}

解答ステップ

(5 x + 8 (\frac{d y}{d x}))^{2}

括弧を削除する:

(a) = a

= (5 x + 8 \frac{d y}{d x})^{2}

完全平方式を適用する:

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

a = 5 x, b = 8 \frac{d y}{d x}

= (5 x)^{2} + 2 \cdot 5 x \cdot 8 \frac{d y}{d x} + (8 \frac{d y}{d x})^{2}

簡素化

(5 x)^{2} + 2 \cdot 5 x \cdot 8 \frac{d y}{d x} + (8 \frac{d y}{d x})^{2} : 25 x^{2} + 80 x \frac{d y}{d x} + 64 \frac{d y}{d x}^{2}

= 25 x^{2} + 80 x \frac{d y}{d x} + 64 \frac{d y}{d x}^{2}