What is expand (y-1/3)^4 ?

The solution to expand (y-1/3)^4 is y^4-(4y^3)/3+(2y^2)/3-(4y)/(27)+1/81

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expand (y-1/3)^4

expand

(y - \frac{1}{3})^{4}

y^{4} - \frac{4 y ^{3}}{3} + \frac{2 y ^{2}}{3} - \frac{4 y}{27} + \frac{1}{81}

Solution steps

(y - \frac{1}{3})^{4}

Apply binomial theorem:

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

a = y, b = - \frac{1}{3}

= i = 0 \sum 4 (i 4) y^{(4 - i)} (- \frac{1}{3})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} y^{4} (- \frac{1}{3})^{0} : y^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} y^{3} (- \frac{1}{3})^{1} : - \frac{4 y ^{3}}{3}

Simplify

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

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} y^{1} (- \frac{1}{3})^{3} : - \frac{4 y}{27}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} y^{0} (- \frac{1}{3})^{4} : \frac{1}{81}

= y^{4} - \frac{4 y ^{3}}{3} + \frac{2 y ^{2}}{3} - \frac{4 y}{27} + \frac{1}{81}

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

\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)

What is expand (y-1/3)^4 ?
The solution to expand (y-1/3)^4 is y^4-(4y^3)/3+(2y^2)/3-(4y)/(27)+1/81