展开 ((15p+4q)^2)/(400)

解答

展开

\frac{( 15 p + 4 q ) ^{2}}{400}

\frac{9 p ^{2}}{16} + \frac{3 pq}{10} + \frac{q ^{2}}{25}

求解步骤

\frac{( 15 p + 4 q ) ^{2}}{400}

(15 p + 4 q)^{2} = 225 p^{2} + 120 pq + 16 q^{2}

= \frac{225 p ^{2} + 120 pq + 16 q ^{2}}{400}

使用分式法则:

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

\frac{225 p ^{2} + 120 pq + 16 q ^{2}}{400} = \frac{225 p ^{2}}{400} + \frac{120 pq}{400} + \frac{16 q ^{2}}{400}

= \frac{225 p ^{2}}{400} + \frac{120 pq}{400} + \frac{16 q ^{2}}{400}

消掉

\frac{225 p ^{2}}{400} : \frac{9 p ^{2}}{16}

= \frac{9 p ^{2}}{16} + \frac{120 pq}{400} + \frac{16 q ^{2}}{400}

消掉

\frac{120 pq}{400} : \frac{3 pq}{10}

= \frac{9 p ^{2}}{16} + \frac{3 pq}{10} + \frac{16 q ^{2}}{400}

消掉

\frac{16 q ^{2}}{400} : \frac{q ^{2}}{25}

= \frac{9 p ^{2}}{16} + \frac{3 pq}{10} + \frac{q ^{2}}{25}

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