What is expand-(15(x-12)(x-14)(x-18))/(32) ?

The solution to expand-(15(x-12)(x-14)(x-18))/(32) is -(15x^3}{32}+\frac{165x^2)/8-(2385x)/8+2835/2

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expand-(15(x-12)(x-14)(x-18))/(32)

expand

- \frac{15 ( x - 12 ) ( x - 14 ) ( x - 18 )}{32}

- \frac{15 x ^{3}}{32} + \frac{165 x ^{2}}{8} - \frac{2385 x}{8} + \frac{2835}{2}

Solution steps

- \frac{15 ( x - 12 ) ( x - 14 ) ( x - 18 )}{32}

Expand

15 (x - 12) (x - 14) (x - 18) : 15 x^{3} - 660 x^{2} + 9540 x - 45360

= - \frac{15 x ^{3} - 660 x ^{2} + 9540 x - 45360}{32}

Apply the fraction rule:

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

\frac{15 x ^{3} - 660 x ^{2} + 9540 x - 45360}{32} = - (\frac{15 x ^{3}}{32}) - (- \frac{660 x ^{2}}{32}) - (\frac{9540 x}{32}) - (- \frac{45360}{32})

= - (\frac{15 x ^{3}}{32}) - (- \frac{660 x ^{2}}{32}) - (\frac{9540 x}{32}) - (- \frac{45360}{32})

Remove parentheses:

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

= - \frac{15 x ^{3}}{32} + \frac{660 x ^{2}}{32} - \frac{9540 x}{32} + \frac{45360}{32}

Cancel

\frac{660 x ^{2}}{32} : \frac{165 x ^{2}}{8}

= - \frac{15 x ^{3}}{32} + \frac{165 x ^{2}}{8} - \frac{9540 x}{32} + \frac{45360}{32}

Cancel

\frac{9540 x}{32} : \frac{2385 x}{8}

= - \frac{15 x ^{3}}{32} + \frac{165 x ^{2}}{8} - \frac{2385 x}{8} + \frac{45360}{32}

Cancel

\frac{45360}{32} : \frac{2835}{2}

= - \frac{15 x ^{3}}{32} + \frac{165 x ^{2}}{8} - \frac{2385 x}{8} + \frac{2835}{2}

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What is expand-(15(x-12)(x-14)(x-18))/(32) ?
The solution to expand-(15(x-12)(x-14)(x-18))/(32) is -(15x^3}{32}+\frac{165x^2)/8-(2385x)/8+2835/2