What is expand ((x-3)*(x-5)*(x-7))/(48) ?

The solution to expand ((x-3)*(x-5)*(x-7))/(48) is (x^3)/(48)-(5x^2)/(16)+(71x)/(48)-35/16

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expand ((x-3)(x-5)(x-7))/(48)

expand

\frac{( x - 3 ) \cdot ( x - 5 ) \cdot ( x - 7 )}{48}

\frac{x ^{3}}{48} - \frac{5 x ^{2}}{16} + \frac{71 x}{48} - \frac{35}{16}

Solution steps

\frac{( x - 3 ) ( x - 5 ) ( x - 7 )}{48}

Expand

(x - 3) (x - 5) (x - 7) : x^{3} - 15 x^{2} + 71 x - 105

= \frac{x ^{3} - 15 x ^{2} + 71 x - 105}{48}

Apply the fraction rule:

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

\frac{x ^{3} - 15 x ^{2} + 71 x - 105}{48} = \frac{x ^{3}}{48} - \frac{15 x ^{2}}{48} + \frac{71 x}{48} - \frac{105}{48}

= \frac{x ^{3}}{48} - \frac{15 x ^{2}}{48} + \frac{71 x}{48} - \frac{105}{48}

Cancel

\frac{15 x ^{2}}{48} : \frac{5 x ^{2}}{16}

= \frac{x ^{3}}{48} - \frac{5 x ^{2}}{16} + \frac{71 x}{48} - \frac{105}{48}

Cancel

\frac{105}{48} : \frac{35}{16}

= \frac{x ^{3}}{48} - \frac{5 x ^{2}}{16} + \frac{71 x}{48} - \frac{35}{16}

\frac{5 x ^{2} + 60 x - 5}{( x + 1 ) ( x - 4 ) ( x + 5 )}

e^{2 - t} U (t - 1)

\frac{5}{( s + 1 ) ^{3}}

\frac{4 r ^{3} π - 2048 π}{3 ( r - 8 )}

e^{3 x} (e^{- 5 x} + 7)

What is expand ((x-3)*(x-5)*(x-7))/(48) ?
The solution to expand ((x-3)*(x-5)*(x-7))/(48) is (x^3)/(48)-(5x^2)/(16)+(71x)/(48)-35/16