What is expand ((x-1)(x-2)(x-3))/((0-1)(0-2)(0-3)) ?

The solution to expand ((x-1)(x-2)(x-3))/((0-1)(0-2)(0-3)) is -(x^3)/6+x^2-(11x)/6+1

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expand ((x-1)(x-2)(x-3))/((0-1)(0-2)(0-3))

expand

\frac{( x - 1 ) ( x - 2 ) ( x - 3 )}{( 0 - 1 ) ( 0 - 2 ) ( 0 - 3 )}

- \frac{x ^{3}}{6} + x^{2} - \frac{11 x}{6} + 1

Solution steps

\frac{( x - 1 ) ( x - 2 ) ( x - 3 )}{( 0 - 1 ) ( 0 - 2 ) ( 0 - 3 )}

(0 - 1) (0 - 2) (0 - 3) = - 6

= \frac{( x - 1 ) ( x - 2 ) ( x - 3 )}{- 6}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{( x - 1 ) ( x - 2 ) ( x - 3 )}{6}

Expand

(x - 1) (x - 2) (x - 3) : x^{3} - 6 x^{2} + 11 x - 6

= - \frac{x ^{3} - 6 x ^{2} + 11 x - 6}{6}

Apply the fraction rule:

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

\frac{x ^{3} - 6 x ^{2} + 11 x - 6}{6} = - (\frac{x ^{3}}{6}) - (- \frac{6 x ^{2}}{6}) - (\frac{11 x}{6}) - (- \frac{6}{6})

= - (\frac{x ^{3}}{6}) - (- \frac{6 x ^{2}}{6}) - (\frac{11 x}{6}) - (- \frac{6}{6})

Remove parentheses:

(a) = a, - (- a) = a

= - \frac{x ^{3}}{6} + \frac{6 x ^{2}}{6} - \frac{11 x}{6} + \frac{6}{6}

Divide the numbers:

\frac{6}{6} = 1

= - \frac{x ^{3}}{6} + x^{2} - \frac{11 x}{6} + \frac{6}{6}

Apply rule

\frac{a}{a} = 1

= - \frac{x ^{3}}{6} + x^{2} - \frac{11 x}{6} + 1

e^{a} + e^{a} (x - a)

(1 + cos (α)) (1 + csc (α))

(a + b x + 2 c x^{2} + 3 d x^{3} + 4 e x^{4})^{2}

\frac{4 ( x + 1 )}{5 ( x + 3 )}

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

What is expand ((x-1)(x-2)(x-3))/((0-1)(0-2)(0-3)) ?
The solution to expand ((x-1)(x-2)(x-3))/((0-1)(0-2)(0-3)) is -(x^3)/6+x^2-(11x)/6+1