展開する ((cb+da)(c+d))/(ba)

解

展開する

\frac{( c b + d a ) ( c + d )}{ba}

\frac{c ^{2}}{a} + \frac{c d}{a} + \frac{c d}{b} + \frac{d ^{2}}{b}

解答ステップ

\frac{( c b + d a ) ( c + d )}{ba}

拡張

(c b + d a) (c + d) : c^{2} b + c b d + c d a + d^{2} a

= \frac{c ^{2} b + c b d + c d a + d ^{2} a}{ba}

分数の規則を適用する:

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

\frac{c ^{2} b + c b d + c d a + d ^{2} a}{ba} = \frac{c ^{2} b}{ba} + \frac{c b d}{ba} + \frac{c d a}{ba} + \frac{d ^{2} a}{ba}

= \frac{c ^{2} b}{ba} + \frac{c b d}{ba} + \frac{c d a}{ba} + \frac{d ^{2} a}{ba}

\frac{c ^{2} b}{ba} = \frac{c ^{2}}{a}

\frac{c b d}{ba} = \frac{c d}{a}

\frac{c d a}{ba} = \frac{c d}{b}

\frac{d ^{2} a}{ba} = \frac{d ^{2}}{b}

= \frac{c ^{2}}{a} + \frac{c d}{a} + \frac{c d}{b} + \frac{d ^{2}}{b}