簡約 (F(L/3-x)-(w(5x-2L)^2)/(50))(L/3-x)

解

簡約

(F (\frac{L}{3} - x) - \frac{w ( 5 x - 2 L ) ^{2}}{50}) (\frac{L}{3} - x)

\frac{( - 150 F x + 50 F L - 75 x ^{2} w + 60 w xL - 12 L ^{2} w ) ( - 3 x + L )}{450}

解答ステップ

(F (\frac{L}{3} - x) - \frac{w ( 5 x - 2 L ) ^{2}}{50}) (\frac{L}{3} - x)

簡素化

F (\frac{L}{3} - x) - \frac{w ( 5 x - 2 L ) ^{2}}{50} : \frac{F ( - 3 x + L )}{3} - \frac{w ( 5 x - 2 L ) ^{2}}{50}

= (\frac{F ( - 3 x + L )}{3} - \frac{w ( 5 x - 2 L ) ^{2}}{50}) (\frac{L}{3} - x)

簡素化

\frac{L}{3} - x : \frac{- 3 x + L}{3}

= (\frac{F ( - 3 x + L )}{3} - \frac{w ( 5 x - 2 L ) ^{2}}{50}) \frac{- 3 x + L}{3}

分数の規則を適用する:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( \frac{F ( - 3 x + L )}{3} - \frac{w ( 5 x - 2 L ) ^{2}}{50} ) ( - 3 x + L )}{3}

簡素化

(\frac{F ( - 3 x + L )}{3} - \frac{w ( 5 x - 2 L ) ^{2}}{50}) (- 3 x + L) : \frac{( - F \cdot 150 x + F \cdot 50 L - w \cdot 75 x ^{2} + w \cdot 60 xL - w \cdot 12 L ^{2} ) ( - 3 x + L )}{150}

= \frac{\frac{( - F \cdot 150 x + F \cdot 50 L - w \cdot 75 x ^{2} + w \cdot 60 xL - w \cdot 12 L ^{2} ) ( - 3 x + L )}{150}}{3}

分数の規則を適用する:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{( - F \cdot 150 x + F \cdot 50 L - w \cdot 75 x ^{2} + w \cdot 60 xL - w \cdot 12 L ^{2} ) ( - 3 x + L )}{150 \cdot 3}

数を乗じる:

150 \cdot 3 = 450

= \frac{( - F \cdot 150 x + F \cdot 50 L - w \cdot 75 x ^{2} + w \cdot 60 xL - w \cdot 12 L ^{2} ) ( - 3 x + L )}{450}

= \frac{( - 150 F x + 50 F L - 75 w x ^{2} + 60 w xL - 12 w L ^{2} ) ( - 3 x + L )}{450}

= \frac{( - 150 F x + 50 F L - 75 x ^{2} w + 60 w xL - 12 L ^{2} w ) ( - 3 x + L )}{450}