展开 ((-2x+4y+5)^2)/9

解答

展开

\frac{( - 2 x + 4 y + 5 ) ^{2}}{9}

\frac{4 x ^{2}}{9} - \frac{16 x y}{9} - \frac{20 x}{9} + \frac{16 y ^{2}}{9} + \frac{40 y}{9} + \frac{25}{9}

求解步骤

\frac{( - 2 x + 4 y + 5 ) ^{2}}{9}

(- 2 x + 4 y + 5)^{2} = 4 x^{2} - 16 x y - 20 x + 16 y^{2} + 40 y + 25

= \frac{4 x ^{2} - 16 x y - 20 x + 16 y ^{2} + 40 y + 25}{9}

使用分式法则:

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

\frac{4 x ^{2} - 16 x y - 20 x + 16 y ^{2} + 40 y + 25}{9} = \frac{4 x ^{2}}{9} - \frac{16 x y}{9} - \frac{20 x}{9} + \frac{16 y ^{2}}{9} + \frac{40 y}{9} + \frac{25}{9}

= \frac{4 x ^{2}}{9} - \frac{16 x y}{9} - \frac{20 x}{9} + \frac{16 y ^{2}}{9} + \frac{40 y}{9} + \frac{25}{9}

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