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

The solution to expand 2pir^2*(pir-2pir^2) is -4pi^2r^4+2pi^2r^3

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expand 2pir^2*(pir-2pir^2)

expand

2 π r^{2} \cdot (π r - 2 π r^{2})

- 4 π^{2} r^{4} + 2 π^{2} r^{3}

Solution steps

2 π r^{2} (π r - 2 π r^{2})

Apply the distributive law:

a (b - c) = ab - a c

a = 2 π r^{2}, b = π r, c = 2 π r^{2}

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

= 2 ππ r^{2} r - 2 \cdot 2 ππ r^{2} r^{2}

Simplify

2 ππ r^{2} r - 2 \cdot 2 ππ r^{2} r^{2} : - 4 π^{2} r^{4} + 2 π^{2} r^{3}

= - 4 π^{2} r^{4} + 2 π^{2} r^{3}

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

y^{3} d x - (x + 1) d y

(1 - e^{\frac{x}{25}})^{2}

\frac{( x + 5 ) ( 4 x + 320 )}{x}

(2 + d^{2} e) (2 - d^{2} e)

What is expand 2pir^2*(pir-2pir^2) ?
The solution to expand 2pir^2*(pir-2pir^2) is -4pi^2r^4+2pi^2r^3