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

The solution to expand (z+2/3)^4 is z^4+(8z^3)/3+(8z^2)/3+(32z)/(27)+16/81

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expand (z+2/3)^4

expand

(z + \frac{2}{3})^{4}

z^{4} + \frac{8 z ^{3}}{3} + \frac{8 z ^{2}}{3} + \frac{32 z}{27} + \frac{16}{81}

Solution steps

(z + \frac{2}{3})^{4}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = z, b = \frac{2}{3}

= i = 0 \sum 4 (i 4) z^{(4 - i)} (\frac{2}{3})^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} z^{4} (\frac{2}{3})^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} z^{3} (\frac{2}{3})^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} z^{2} (\frac{2}{3})^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} z^{1} (\frac{2}{3})^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} z^{0} (\frac{2}{3})^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} z^{4} (\frac{2}{3})^{0} : z^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} z^{3} (\frac{2}{3})^{1} : \frac{8 z ^{3}}{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} z^{2} (\frac{2}{3})^{2} : \frac{8 z ^{2}}{3}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} z^{1} (\frac{2}{3})^{3} : \frac{32 z}{27}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} z^{0} (\frac{2}{3})^{4} : \frac{16}{81}

= z^{4} + \frac{8 z ^{3}}{3} + \frac{8 z ^{2}}{3} + \frac{32 z}{27} + \frac{16}{81}

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

(1 + i t)^{2}

e^{3 x} \cdot (3 x^{2} y + 2 x y + y^{3})

e^{2} t (sin (2 t) - 1)

sinh ((x - b) (x - c)) (2 x - c - b)

What is expand (z+2/3)^4 ?
The solution to expand (z+2/3)^4 is z^4+(8z^3)/3+(8z^2)/3+(32z)/(27)+16/81