What is expand 4/3 pi(x+1)^3 ?

The solution to expand 4/3 pi(x+1)^3 is (4pix^3)/3+4pix^2+4pix+(4pi)/3

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expand 4/3 pi(x+1)^3

expand

\frac{4}{3} π (x + 1)^{3}

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

Solution steps

\frac{4}{3} π (x + 1)^{3}

(x + 1)^{3} = x^{3} + 3 x^{2} + 3 x + 1

= π \frac{4}{3} (x^{3} + 3 x^{2} + 3 x + 1)

Multiply fractions:

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

= \frac{4 π}{3} (x^{3} + 3 x^{2} + 3 x + 1)

Distribute parentheses

= \frac{4 π}{3} x^{3} + \frac{4 π}{3} \cdot 3 x^{2} + \frac{4 π}{3} \cdot 3 x + \frac{4 π}{3} \cdot 1

= \frac{4 π}{3} x^{3} + 3 \cdot \frac{4 π}{3} x^{2} + 3 \cdot \frac{4 π}{3} x + 1 \cdot \frac{4 π}{3}

Simplify

\frac{4 π}{3} x^{3} + 3 \cdot \frac{4 π}{3} x^{2} + 3 \cdot \frac{4 π}{3} x + 1 \cdot \frac{4 π}{3} : \frac{4 π x ^{3} + 4 π}{3} + 4 π x^{2} + 4 π x

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

Apply the fraction rule:

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

\frac{4 π x ^{3} + 4 π}{3} = \frac{4 π x ^{3}}{3} + \frac{4 π}{3}

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

Rewrite in standard form

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

\frac{5 - x}{( x - 9 ) ( x - 3 )}

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

- 1^{- 2} + 4

\frac{π ( 3 ^{25} - 1 )}{ln ( 3 )}

\frac{133 ( 1 + 5 )}{2}

What is expand 4/3 pi(x+1)^3 ?
The solution to expand 4/3 pi(x+1)^3 is (4pix^3)/3+4pix^2+4pix+(4pi)/3