展开 (3a^2(b-a)^2)/2

解答

展开

\frac{3 a ^{2} ( b - a ) ^{2}}{2}

\frac{3 a ^{2} b ^{2}}{2} - 3 a^{3} b + \frac{3 a ^{4}}{2}

求解步骤

\frac{3 a ^{2} ( b - a ) ^{2}}{2}

(b - a)^{2} = b^{2} - 2 ab + a^{2}

= \frac{3 a ^{2} ( a ^{2} - 2 ab + b ^{2} )}{2}

乘开

3 a^{2} (b^{2} - 2 ba + a^{2}) : 3 a^{2} b^{2} - 6 a^{3} b + 3 a^{4}

= \frac{3 a ^{2} b ^{2} - 6 a ^{3} b + 3 a ^{4}}{2}

使用分式法则:

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

\frac{3 a ^{2} b ^{2} - 6 a ^{3} b + 3 a ^{4}}{2} = \frac{3 a ^{2} b ^{2}}{2} - \frac{6 a ^{3} b}{2} + \frac{3 a ^{4}}{2}

= \frac{3 a ^{2} b ^{2}}{2} - \frac{6 a ^{3} b}{2} + \frac{3 a ^{4}}{2}

数字相除:

\frac{6}{2} = 3

= \frac{3 a ^{2} b ^{2}}{2} - 3 a^{3} b + \frac{3 a ^{4}}{2}

e x p an d 2 (x + 2 - 2 ln (x + 2))

e x p an d \frac{2 x + 1}{( x - 2 ) ^{2}}

e x p an d (e^{2 y} - 1) \cdot (e^{2 x} + 1)

e x p an d \frac{2 x ^{2} - 8 x + 5}{( x - 2 ) ^{2}}

e x p an d f (x) (x = a x^{2} + b x + c)