What is expand (4pi(3t^2+4t)^3)/3 ?

The solution to expand (4pi(3t^2+4t)^3)/3 is 36pit^6+144pit^5+192pit^4+(256pit^3)/3

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expand (4pi(3t^2+4t)^3)/3

expand

\frac{4 π ( 3 t ^{2} + 4 t ) ^{3}}{3}

36 π t^{6} + 144 π t^{5} + 192 π t^{4} + \frac{256 π t ^{3}}{3}

Solution steps

\frac{4 π ( 3 t ^{2} + 4 t ) ^{3}}{3}

(3 t^{2} + 4 t)^{3} = 27 t^{6} + 108 t^{5} + 144 t^{4} + 64 t^{3}

= \frac{4 π ( 27 t ^{6} + 108 t ^{5} + 144 t ^{4} + 64 t ^{3} )}{3}

Expand

4 π (27 t^{6} + 108 t^{5} + 144 t^{4} + 64 t^{3}) : 108 π t^{6} + 432 π t^{5} + 576 π t^{4} + 256 π t^{3}

= \frac{108 π t ^{6} + 432 π t ^{5} + 576 π t ^{4} + 256 π t ^{3}}{3}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{108 π t ^{6} + 432 π t ^{5} + 576 π t ^{4} + 256 π t ^{3}}{3} = \frac{108 π t ^{6}}{3} + \frac{432 π t ^{5}}{3} + \frac{576 π t ^{4}}{3} + \frac{256 π t ^{3}}{3}

= \frac{108 π t ^{6}}{3} + \frac{432 π t ^{5}}{3} + \frac{576 π t ^{4}}{3} + \frac{256 π t ^{3}}{3}

Divide the numbers:

\frac{108}{3} = 36

= 36 π t^{6} + \frac{432 π t ^{5}}{3} + \frac{576 π t ^{4}}{3} + \frac{256 π t ^{3}}{3}

Divide the numbers:

\frac{432}{3} = 144

= 36 π t^{6} + 144 π t^{5} + \frac{576 π t ^{4}}{3} + \frac{256 π t ^{3}}{3}

Divide the numbers:

\frac{576}{3} = 192

= 36 π t^{6} + 144 π t^{5} + 192 π t^{4} + \frac{256 π t ^{3}}{3}

(1 + 2 x) e^{x}

\frac{x + 7}{( x + 1 ) ( x - 3 )}

- \frac{36}{x ( x + 9 h )}

W (e x, e - x)

- \frac{( x - 2 ) ( x + 8 )}{21}

What is expand (4pi(3t^2+4t)^3)/3 ?
The solution to expand (4pi(3t^2+4t)^3)/3 is 36pit^6+144pit^5+192pit^4+(256pit^3)/3