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

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

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expand (((x+1)(x)(x-2))/(-2))*3

expand

(\frac{( x + 1 ) ( x ) ( x - 2 )}{- 2}) \cdot 3

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

Solution steps

(\frac{( x + 1 ) ( x ) ( x - 2 )}{- 2}) \cdot 3

Remove parentheses:

(a) = a

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

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

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

Multiply fractions:

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

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

Expand

(x^{3} - x^{2} - 2 x) \cdot 3 : 3 x^{3} - 3 x^{2} - 6 x

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

Apply the fraction rule:

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

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

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

Remove parentheses:

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

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

Divide the numbers:

\frac{6}{2} = 3

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

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