What is expand pir^2(108-2pir) ?

The solution to expand pir^2(108-2pir) is -2pi^2r^3+108pir^2

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expand pir^2(108-2pir)

expand

π r^{2} (108 - 2 π r)

- 2 π^{2} r^{3} + 108 π r^{2}

Solution steps

π r^{2} (108 - 2 π r)

Apply the distributive law:

a (b - c) = ab - a c

a = π r^{2}, b = 108, c = 2 π r

= π r^{2} \cdot 108 - π r^{2} \cdot 2 π r

= 108 π r^{2} - 2 ππ r^{2} r

Simplify

108 π r^{2} - 2 ππ r^{2} r : - 2 π^{2} r^{3} + 108 π r^{2}

= - 2 π^{2} r^{3} + 108 π r^{2}

2 (arctan (tan (t)) + \frac{π}{4})

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

(1 + 3 \cdot i)^{4}

\frac{9}{4 x ( 5 x + 3 )}

\frac{2 ( x + 1 ) ( x - 1 )}{x + 3}

What is expand pir^2(108-2pir) ?
The solution to expand pir^2(108-2pir) is -2pi^2r^3+108pir^2