What is expand ((x-3)^5)/6 ?

The solution to expand ((x-3)^5)/6 is (x^5)/6-(5x^4)/2+15x^3-45x^2+(135x)/2-81/2

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expand ((x-3)^5)/6

expand

\frac{( x - 3 ) ^{5}}{6}

\frac{x ^{5}}{6} - \frac{5 x ^{4}}{2} + 15 x^{3} - 45 x^{2} + \frac{135 x}{2} - \frac{81}{2}

Solution steps

\frac{( x - 3 ) ^{5}}{6}

(x - 3)^{5} = x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 243

= \frac{x ^{5} - 15 x ^{4} + 90 x ^{3} - 270 x ^{2} + 405 x - 243}{6}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{5} - 15 x ^{4} + 90 x ^{3} - 270 x ^{2} + 405 x - 243}{6} = \frac{x ^{5}}{6} - \frac{15 x ^{4}}{6} + \frac{90 x ^{3}}{6} - \frac{270 x ^{2}}{6} + \frac{405 x}{6} - \frac{243}{6}

= \frac{x ^{5}}{6} - \frac{15 x ^{4}}{6} + \frac{90 x ^{3}}{6} - \frac{270 x ^{2}}{6} + \frac{405 x}{6} - \frac{243}{6}

\frac{15 x ^{4}}{6} = \frac{5 x ^{4}}{2}

\frac{90 x ^{3}}{6} = 15 x^{3}

\frac{270 x ^{2}}{6} = 45 x^{2}

\frac{405 x}{6} = \frac{135 x}{2}

\frac{243}{6} = \frac{81}{2}

= \frac{x ^{5}}{6} - \frac{5 x ^{4}}{2} + 15 x^{3} - 45 x^{2} + \frac{135 x}{2} - \frac{81}{2}

(a + \frac{2}{3} b x)^{3}

\frac{( x - 2 ) ^{2}}{4}

(1 + sin (x))^{(2)} + (ln (x))^{(2 x)}

3 \cdot 5 \cdot (2 \cdot 2 - 7)

2 (1 + cos (θ))^{2}

What is expand ((x-3)^5)/6 ?
The solution to expand ((x-3)^5)/6 is (x^5)/6-(5x^4)/2+15x^3-45x^2+(135x)/2-81/2