展开 ((x+4)^4)/4

解答

展开

\frac{( x + 4 ) ^{4}}{4}

\frac{x ^{4}}{4} + 4 x^{3} + 24 x^{2} + 64 x + 64

求解步骤

\frac{( x + 4 ) ^{4}}{4}

(x + 4)^{4} = x^{4} + 16 x^{3} + 96 x^{2} + 256 x + 256

= \frac{x ^{4} + 16 x ^{3} + 96 x ^{2} + 256 x + 256}{4}

使用分式法则:

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

\frac{x ^{4} + 16 x ^{3} + 96 x ^{2} + 256 x + 256}{4} = \frac{x ^{4}}{4} + \frac{16 x ^{3}}{4} + \frac{96 x ^{2}}{4} + \frac{256 x}{4} + \frac{256}{4}

= \frac{x ^{4}}{4} + \frac{16 x ^{3}}{4} + \frac{96 x ^{2}}{4} + \frac{256 x}{4} + \frac{256}{4}

\frac{16 x ^{3}}{4} = 4 x^{3}

\frac{96 x ^{2}}{4} = 24 x^{2}

\frac{256 x}{4} = 64 x

\frac{256}{4} = 64

= \frac{x ^{4}}{4} + 4 x^{3} + 24 x^{2} + 64 x + 64

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