What is expand (3-1/3 x)^5 ?

The solution to expand (3-1/3 x)^5 is 243-135x+30x^2-(10x^3)/3+(5x^4)/(27)-(x^5)/(243)

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expand (3-1/3 x)^5

expand

(3 - \frac{1}{3} x)^{5}

243 - 135 x + 30 x^{2} - \frac{10 x ^{3}}{3} + \frac{5 x ^{4}}{27} - \frac{x ^{5}}{243}

Solution steps

(3 - \frac{1}{3} x)^{5}

Apply binomial theorem:

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

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

= i = 0 \sum 5 (i 5) \cdot 3^{(5 - i)} (- \frac{1}{3} x)^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 3^{5} (- \frac{1}{3} x)^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 3^{4} (- \frac{1}{3} x)^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 3^{3} (- \frac{1}{3} x)^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 3^{2} (- \frac{1}{3} x)^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 3^{1} (- \frac{1}{3} x)^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 3^{0} (- \frac{1}{3} x)^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 3^{5} (- \frac{1}{3} x)^{0} : 243

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 3^{4} (- \frac{1}{3} x)^{1} : - 135 x

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 3^{3} (- \frac{1}{3} x)^{2} : 30 x^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 3^{2} (- \frac{1}{3} x)^{3} : - \frac{10 x ^{3}}{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 3^{1} (- \frac{1}{3} x)^{4} : \frac{5 x ^{4}}{27}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 3^{0} (- \frac{1}{3} x)^{5} : - \frac{x ^{5}}{243}

= 243 - 135 x + 30 x^{2} - \frac{10 x ^{3}}{3} + \frac{5 x ^{4}}{27} - \frac{x ^{5}}{243}

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

(e^{x} - e^{- x})^{2}

(1 - i) (1 + i)

t^{2} (1 + e^{- a t})

(\frac{5 m}{4} + \frac{2}{3}) (\frac{5 m}{4} - \frac{2}{3})

What is expand (3-1/3 x)^5 ?
The solution to expand (3-1/3 x)^5 is 243-135x+30x^2-(10x^3)/3+(5x^4)/(27)-(x^5)/(243)