What is expand ((x+1)(x-1)(x-2))/2 ?

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

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expand ((x+1)(x-1)(x-2))/2

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Apply rule

\frac{a}{a} = 1

\frac{2}{2} = 1

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

Divide the numbers:

\frac{2}{2} = 1

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

\frac{s}{( s ^{2} + w ^{2} ) ( s ^{2} + 1 )}

\frac{i}{( x + i y ) ^{2}}

4 x (x + 3) (x - 3)

(x + \frac{1}{4} y)^{5}

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