What is expand-1/6 (x-pi/2)^3 ?

The solution to expand-1/6 (x-pi/2)^3 is -(x^3)/6+(pix^2)/4-(pi^2x)/8+(pi^3)/(48)

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expand-1/6 (x-pi/2)^3

expand

- \frac{1}{6} (x - \frac{π}{2})^{3}

- \frac{x ^{3}}{6} + \frac{π x ^{2}}{4} - \frac{π ^{2} x}{8} + \frac{π ^{3}}{48}

Solution steps

- \frac{1}{6} (x - \frac{π}{2})^{3}

(x - \frac{π}{2})^{3} = x^{3} - \frac{3 π x ^{2}}{2} + \frac{3 π ^{2} x}{4} - \frac{π ^{3}}{8}

= - \frac{1}{6} (x^{3} - \frac{3 π x ^{2}}{2} + \frac{3 π ^{2} x}{4} - \frac{π ^{3}}{8})

Distribute parentheses

= (- \frac{1}{6}) x^{3} + (- \frac{1}{6}) (- \frac{3 π x ^{2}}{2}) + (- \frac{1}{6}) \frac{3 π ^{2} x}{4} + (- \frac{1}{6}) (- \frac{π ^{3}}{8})

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= - \frac{1}{6} x^{3} + \frac{1}{6} \cdot \frac{3 π x ^{2}}{2} - \frac{1}{6} \cdot \frac{3 π ^{2} x}{4} + \frac{1}{6} \cdot \frac{π ^{3}}{8}

Simplify

- \frac{1}{6} x^{3} + \frac{1}{6} \cdot \frac{3 π x ^{2}}{2} - \frac{1}{6} \cdot \frac{3 π ^{2} x}{4} + \frac{1}{6} \cdot \frac{π ^{3}}{8} : - \frac{x ^{3}}{6} + \frac{π x ^{2}}{4} - \frac{π ^{2} x}{8} + \frac{π ^{3}}{48}

= - \frac{x ^{3}}{6} + \frac{π x ^{2}}{4} - \frac{π ^{2} x}{8} + \frac{π ^{3}}{48}

\frac{d ^{2}}{d x ^{2}} ((y) (3 x^{6} + 7 x^{4} - 2 x^{2} + 5))

- 0.6 (10.3229 - 5)^{2} + 17

\frac{2 ( 32 - 771 )}{23}

5 (2 x e^{x} + e^{x} x^{2})

(tan (x) - sin (x) sin (y)) d x + cos (x) cos (y) d y

What is expand-1/6 (x-pi/2)^3 ?
The solution to expand-1/6 (x-pi/2)^3 is -(x^3)/6+(pix^2)/4-(pi^2x)/8+(pi^3)/(48)