展开 ((h+1)(4h^2+8h+3))/3

解答

展开

\frac{( h + 1 ) ( 4 h ^{2} + 8 h + 3 )}{3}

\frac{4 h ^{3}}{3} + 4 h^{2} + \frac{11 h}{3} + 1

求解步骤

\frac{( h + 1 ) ( 4 h ^{2} + 8 h + 3 )}{3}

乘开

(h + 1) (4 h^{2} + 8 h + 3) : 4 h^{3} + 12 h^{2} + 11 h + 3

= \frac{4 h ^{3} + 12 h ^{2} + 11 h + 3}{3}

使用分式法则:

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

\frac{4 h ^{3} + 12 h ^{2} + 11 h + 3}{3} = \frac{4 h ^{3}}{3} + \frac{12 h ^{2}}{3} + \frac{11 h}{3} + \frac{3}{3}

= \frac{4 h ^{3}}{3} + \frac{12 h ^{2}}{3} + \frac{11 h}{3} + \frac{3}{3}

使用法则

\frac{a}{a} = 1

\frac{3}{3} = 1

= \frac{4 h ^{3}}{3} + \frac{12 h ^{2}}{3} + \frac{11 h}{3} + 1

数字相除:

\frac{12}{3} = 4

= \frac{4 h ^{3}}{3} + 4 h^{2} + \frac{11 h}{3} + 1

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