What is expand ((5x-30)(x-6)^2)/6 ?

The solution to expand ((5x-30)(x-6)^2)/6 is (5x^3)/6-15x^2+90x-180

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expand ((5x-30)(x-6)^2)/6

expand

\frac{( 5 x - 30 ) ( x - 6 ) ^{2}}{6}

\frac{5 x ^{3}}{6} - 15 x^{2} + 90 x - 180

Solution steps

\frac{( 5 x - 30 ) ( x - 6 ) ^{2}}{6}

(x - 6)^{2} = x^{2} - 12 x + 36

= \frac{( 5 x - 30 ) ( x ^{2} - 12 x + 36 )}{6}

Expand

(5 x - 30) (x^{2} - 12 x + 36) : 5 x^{3} - 90 x^{2} + 540 x - 1080

= \frac{5 x ^{3} - 90 x ^{2} + 540 x - 1080}{6}

Apply the fraction rule:

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

\frac{5 x ^{3} - 90 x ^{2} + 540 x - 1080}{6} = \frac{5 x ^{3}}{6} - \frac{90 x ^{2}}{6} + \frac{540 x}{6} - \frac{1080}{6}

= \frac{5 x ^{3}}{6} - \frac{90 x ^{2}}{6} + \frac{540 x}{6} - \frac{1080}{6}

Divide the numbers:

\frac{90}{6} = 15

= \frac{5 x ^{3}}{6} - 15 x^{2} + \frac{540 x}{6} - \frac{1080}{6}

Divide the numbers:

\frac{540}{6} = 90

= \frac{5 x ^{3}}{6} - 15 x^{2} + 90 x - \frac{1080}{6}

Divide the numbers:

\frac{1080}{6} = 180

= \frac{5 x ^{3}}{6} - 15 x^{2} + 90 x - 180

\frac{1}{x ^{3} ( x - a )}

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

(3 x - 2 y = - 1, 0) (4 x + 3 y = - 2)

\frac{( x + y ) h}{2}

\frac{x + 7}{( x + 8 ) ( x + 5 )}

What is expand ((5x-30)(x-6)^2)/6 ?
The solution to expand ((5x-30)(x-6)^2)/6 is (5x^3)/6-15x^2+90x-180