展开 ((x^2+4x+3)(x+1))/(36)

解答

展开

\frac{( x ^{2} + 4 x + 3 ) ( x + 1 )}{36}

\frac{x ^{3}}{36} + \frac{5 x ^{2}}{36} + \frac{7 x}{36} + \frac{1}{12}

求解步骤

\frac{( x ^{2} + 4 x + 3 ) ( x + 1 )}{36}

乘开

(x^{2} + 4 x + 3) (x + 1) : x^{3} + 5 x^{2} + 7 x + 3

= \frac{x ^{3} + 5 x ^{2} + 7 x + 3}{36}

使用分式法则:

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

\frac{x ^{3} + 5 x ^{2} + 7 x + 3}{36} = \frac{x ^{3}}{36} + \frac{5 x ^{2}}{36} + \frac{7 x}{36} + \frac{3}{36}

= \frac{x ^{3}}{36} + \frac{5 x ^{2}}{36} + \frac{7 x}{36} + \frac{3}{36}

消掉

\frac{3}{36} : \frac{1}{12}

= \frac{x ^{3}}{36} + \frac{5 x ^{2}}{36} + \frac{7 x}{36} + \frac{1}{12}

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