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

The solution to expand (4pi)/3 (r+4)^3 is (4pir^3)/3+16pir^2+64pir+(256pi)/3

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expand (4pi)/3 (r+4)^3

expand

\frac{4 π}{3} (r + 4)^{3}

\frac{4 π r ^{3}}{3} + 16 π r^{2} + 64 π r + \frac{256 π}{3}

Solution steps

\frac{4 π}{3} (r + 4)^{3}

(r + 4)^{3} = r^{3} + 12 r^{2} + 48 r + 64

= \frac{4 π}{3} (r^{3} + 12 r^{2} + 48 r + 64)

Distribute parentheses

= \frac{4 π}{3} r^{3} + \frac{4 π}{3} \cdot 12 r^{2} + \frac{4 π}{3} \cdot 48 r + \frac{4 π}{3} \cdot 64

= \frac{4 π}{3} r^{3} + 12 \cdot \frac{4 π}{3} r^{2} + 48 \cdot \frac{4 π}{3} r + 64 \cdot \frac{4 π}{3}

Simplify

\frac{4 π}{3} r^{3} + 12 \cdot \frac{4 π}{3} r^{2} + 48 \cdot \frac{4 π}{3} r + 64 \cdot \frac{4 π}{3} : \frac{4 π r ^{3} + 256 π}{3} + 16 π r^{2} + 64 π r

= \frac{4 π r ^{3} + 256 π}{3} + 16 π r^{2} + 64 π r

Apply the fraction rule:

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

\frac{4 π r ^{3} + 256 π}{3} = \frac{4 π r ^{3}}{3} + \frac{256 π}{3}

= \frac{4 π r ^{3}}{3} + \frac{256 π}{3} + 16 π r^{2} + 64 π r

Rewrite in standard form

= \frac{4 π r ^{3}}{3} + 16 π r^{2} + 64 π r + \frac{256 π}{3}

cos (2 (k + 1))

3 x^{2} + ln (x) \cdot (2 x + ln (x))

(x^{2} y + 4 y) \cdot e^{y^{2}}

a \cdot b - (c + d) \cdot e

\frac{( 8 x + 5 ) ^{2}}{16}

What is expand (4pi)/3 (r+4)^3 ?
The solution to expand (4pi)/3 (r+4)^3 is (4pir^3)/3+16pir^2+64pir+(256pi)/3