展开 pi/3 ((18+y)(3+y/6)^2-(21*3)^2)y

解答

展开

\frac{π}{3} ((18 + y) (3 + \frac{y}{6})^{2} - (21 \cdot 3)^{2}) y

\frac{π y ^{4}}{108} + \frac{π y ^{3}}{2} + 9 π y^{2} - 1269 π y

求解步骤

\frac{π}{3} ((18 + y) (3 + \frac{y}{6})^{2} - (21 \cdot 3)^{2}) y

= \frac{π}{3} y ((18 + y) (3 + \frac{y}{6})^{2} - (21 \cdot 3)^{2})

使用分配律:

a (b - c) = ab - a c

a = \frac{π}{3} y, b = (18 + y) (3 + \frac{y}{6})^{2}, c = (21 \cdot 3)^{2}

= \frac{π}{3} y (18 + y) (3 + \frac{y}{6})^{2} - \frac{π}{3} y (21 \cdot 3)^{2}

= \frac{π}{3} y (18 + y) (3 + \frac{y}{6})^{2} - \frac{π}{3} (21 \cdot 3)^{2} y

化简

\frac{π}{3} y (18 + y) (3 + \frac{y}{6})^{2} - \frac{π}{3} (21 \cdot 3)^{2} y : \frac{π y ^{4}}{108} + \frac{π y ^{3}}{2} + 9 π y^{2} - 1269 π y

= \frac{π y ^{4}}{108} + \frac{π y ^{3}}{2} + 9 π y^{2} - 1269 π y

s im pl i f y (1 + i t + t^{2})^{3}

e x p an d \frac{5 x ^{2}}{( x ^{2} - 9 ) ^{2}}

s im pl i f y 4 (5 - sin (x))

e x p an d 7 (6 + 4)

e x p an d (2 x y) (cos (t)) + (x^{2} - 2 y) (e^{t})