展开 (4(r+1)^3)/3

解答

展开

\frac{4 ( r + 1 ) ^{3}}{3}

\frac{4 r ^{3}}{3} + 4 r^{2} + 4 r + \frac{4}{3}

求解步骤

\frac{4 ( r + 1 ) ^{3}}{3}

(r + 1)^{3} = r^{3} + 3 r^{2} + 3 r + 1

= \frac{4 ( r ^{3} + 3 r ^{2} + 3 r + 1 )}{3}

乘开

4 (r^{3} + 3 r^{2} + 3 r + 1) : 4 r^{3} + 12 r^{2} + 12 r + 4

= \frac{4 r ^{3} + 12 r ^{2} + 12 r + 4}{3}

使用分式法则:

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

\frac{4 r ^{3} + 12 r ^{2} + 12 r + 4}{3} = \frac{4 r ^{3}}{3} + \frac{12 r ^{2}}{3} + \frac{12 r}{3} + \frac{4}{3}

= \frac{4 r ^{3}}{3} + \frac{12 r ^{2}}{3} + \frac{12 r}{3} + \frac{4}{3}

数字相除:

\frac{12}{3} = 4

= \frac{4 r ^{3}}{3} + 4 r^{2} + 4 r + \frac{4}{3}

e x p an d (a x^{2} y^{4} e^{x^{3} y^{4}} + \frac{3}{x ^{2} + 1}) d x

e x p an d (4 - e^{x}) e^{x}

e x p an d \frac{( 2 x ^{2} + x ) ^{2}}{4}

e x p an d \frac{s}{( s + 2 ) ^{2} ( s ^{2} + 25 )}

e x p an d - \frac{( r + θ ) ( r - θ )}{θ ^{2}}