展开 (x^2(8y^3+3x)^2)/(16)

解答

展开

\frac{x ^{2} ( 8 y ^{3} + 3 x ) ^{2}}{16}

4 x^{2} y^{6} + 3 x^{3} y^{3} + \frac{9 x ^{4}}{16}

求解步骤

\frac{x ^{2} ( 8 y ^{3} + 3 x ) ^{2}}{16}

(8 y^{3} + 3 x)^{2} = 64 y^{6} + 48 x y^{3} + 9 x^{2}

= \frac{x ^{2} ( 9 x ^{2} + 48 x y ^{3} + 64 y ^{6} )}{16}

乘开

x^{2} (64 y^{6} + 48 x y^{3} + 9 x^{2}) : 64 x^{2} y^{6} + 48 x^{3} y^{3} + 9 x^{4}

= \frac{64 x ^{2} y ^{6} + 48 x ^{3} y ^{3} + 9 x ^{4}}{16}

使用分式法则:

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

\frac{64 x ^{2} y ^{6} + 48 x ^{3} y ^{3} + 9 x ^{4}}{16} = \frac{64 x ^{2} y ^{6}}{16} + \frac{48 x ^{3} y ^{3}}{16} + \frac{9 x ^{4}}{16}

= \frac{64 x ^{2} y ^{6}}{16} + \frac{48 x ^{3} y ^{3}}{16} + \frac{9 x ^{4}}{16}

数字相除:

\frac{64}{16} = 4

= 4 x^{2} y^{6} + \frac{48 x ^{3} y ^{3}}{16} + \frac{9 x ^{4}}{16}

数字相除:

\frac{48}{16} = 3

= 4 x^{2} y^{6} + 3 x^{3} y^{3} + \frac{9 x ^{4}}{16}

e x p an d \frac{1}{( s ^{2} + a ^{2} ) \cdot ( s ^{2} + b ^{2} )}

\frac{d ^{2}}{d y ^{2}} ((f (x)) (x (y - sin (y))))

e x p an d \frac{4 x ^{2} - 24 x - 52}{( x - 3 ) ^{2}}

e x p an d (2 i + 1)^{3} - (2 j + 1)^{3}

e x p an d 4 x - 2 (x - 2 = - 9 + 4 x + 7)