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

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

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expand (x-pi/2)^3

expand

(x - \frac{π}{2})^{3}

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

Solution steps

(x - \frac{π}{2})^{3}

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

a = x, b = \frac{π}{2}

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

Simplify

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

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

(3 - 2 x)^{2}

(5 c + \frac{2}{3}) (5 c - \frac{2}{3})

\frac{( x - 5 ) ( x + 2 )}{x + 1}

(2 + cos (θ))^{2}

\frac{z + 1}{z ^{2} ( z - 1 )}

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