展开 (x^4(16x^2y^6+3)^2)/(16)

解答

展开

\frac{x ^{4} ( 16 x ^{2} y ^{6} + 3 ) ^{2}}{16}

16 x^{8} y^{12} + 6 x^{6} y^{6} + \frac{9 x ^{4}}{16}

求解步骤

\frac{x ^{4} ( 16 x ^{2} y ^{6} + 3 ) ^{2}}{16}

(16 x^{2} y^{6} + 3)^{2} = 256 x^{4} y^{12} + 96 x^{2} y^{6} + 9

= \frac{x ^{4} ( 256 x ^{4} y ^{12} + 96 x ^{2} y ^{6} + 9 )}{16}

乘开

x^{4} (256 x^{4} y^{12} + 96 x^{2} y^{6} + 9) : 256 x^{8} y^{12} + 96 x^{6} y^{6} + 9 x^{4}

= \frac{256 x ^{8} y ^{12} + 96 x ^{6} y ^{6} + 9 x ^{4}}{16}

使用分式法则:

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

\frac{256 x ^{8} y ^{12} + 96 x ^{6} y ^{6} + 9 x ^{4}}{16} = \frac{256 x ^{8} y ^{12}}{16} + \frac{96 x ^{6} y ^{6}}{16} + \frac{9 x ^{4}}{16}

= \frac{256 x ^{8} y ^{12}}{16} + \frac{96 x ^{6} y ^{6}}{16} + \frac{9 x ^{4}}{16}

数字相除:

\frac{256}{16} = 16

= 16 x^{8} y^{12} + \frac{96 x ^{6} y ^{6}}{16} + \frac{9 x ^{4}}{16}

数字相除:

\frac{96}{16} = 6

= 16 x^{8} y^{12} + 6 x^{6} y^{6} + \frac{9 x ^{4}}{16}

e x p an d 38

\frac{d}{d t} ((z (t, x, y)) (x^{2} + y^{2}))

e x p an d (5 + 4 x) x^{4} e^{4 x} + 5

s im pl i f y 2 (52 + 210)

e x p an d \frac{16}{( s + 2 ) s ^{2}}