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

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

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expand (w-1/3)^4

expand

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

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

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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