What is expand (4/3-x)^4 ?

The solution to expand (4/3-x)^4 is 256/81-(256x}{27}+\frac{32x^2)/3-(16x^3)/3+x^4

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expand (4/3-x)^4

expand

(\frac{4}{3} - x)^{4}

\frac{256}{81} - \frac{256 x}{27} + \frac{32 x ^{2}}{3} - \frac{16 x ^{3}}{3} + x^{4}

Solution steps

(\frac{4}{3} - x)^{4}

Apply binomial theorem:

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

a = \frac{4}{3}, b = - x

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

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (\frac{4}{3})^{4} (- x)^{0} : \frac{256}{81}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (\frac{4}{3})^{3} (- x)^{1} : - \frac{256 x}{27}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (\frac{4}{3})^{2} (- x)^{2} : \frac{32 x ^{2}}{3}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (\frac{4}{3})^{1} (- x)^{3} : - \frac{16 x ^{3}}{3}

Simplify

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

= \frac{256}{81} - \frac{256 x}{27} + \frac{32 x ^{2}}{3} - \frac{16 x ^{3}}{3} + x^{4}

(x^{2} + y^{2}) (7 x + \frac{2}{3})

\frac{3 x ^{2} + 7 x}{( x - 1 ) ( x ^{2} + 4 x + 5 )}

\frac{2 ( x - 2 )}{x - 1}

(x - 8) (\frac{8}{x - 8} + 9 (100 - x))

i (x + i y)^{3}

What is expand (4/3-x)^4 ?
The solution to expand (4/3-x)^4 is 256/81-(256x}{27}+\frac{32x^2)/3-(16x^3)/3+x^4