展开 (x^2y^4(6x-1)^2)/4

解答

展开

\frac{x ^{2} y ^{4} ( 6 x - 1 ) ^{2}}{4}

9 x^{4} y^{4} - 3 x^{3} y^{4} + \frac{x ^{2} y ^{4}}{4}

求解步骤

\frac{x ^{2} y ^{4} ( 6 x - 1 ) ^{2}}{4}

(6 x - 1)^{2} = 36 x^{2} - 12 x + 1

= \frac{x ^{2} y ^{4} ( 36 x ^{2} - 12 x + 1 )}{4}

乘开

x^{2} y^{4} (36 x^{2} - 12 x + 1) : 36 x^{4} y^{4} - 12 x^{3} y^{4} + x^{2} y^{4}

= \frac{36 x ^{4} y ^{4} - 12 x ^{3} y ^{4} + x ^{2} y ^{4}}{4}

使用分式法则:

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

\frac{36 x ^{4} y ^{4} - 12 x ^{3} y ^{4} + x ^{2} y ^{4}}{4} = \frac{36 x ^{4} y ^{4}}{4} - \frac{12 x ^{3} y ^{4}}{4} + \frac{x ^{2} y ^{4}}{4}

= \frac{36 x ^{4} y ^{4}}{4} - \frac{12 x ^{3} y ^{4}}{4} + \frac{x ^{2} y ^{4}}{4}

数字相除:

\frac{36}{4} = 9

= 9 x^{4} y^{4} - \frac{12 x ^{3} y ^{4}}{4} + \frac{x ^{2} y ^{4}}{4}

数字相除:

\frac{12}{4} = 3

= 9 x^{4} y^{4} - 3 x^{3} y^{4} + \frac{x ^{2} y ^{4}}{4}

\frac{d}{d θ} ((x (θ)) (a (θ - sin (θ))))

e x p an d \frac{k ( s + 4 )}{s ( s + 1 ) ( s + 3 )}

s im pl i f y (2 - x - 4)^{2}

e x p an d - e^{x} (e^{2 x} - e^{- x})

e x p an d (3 sin^{2} (θ)) (1 + sin^{2} (θ))