What is expand (sqrt(x)(x-6)^2)/3 ?

The solution to expand (sqrt(x)(x-6)^2)/3 is (x^2sqrt(x))/3-4xsqrt(x)+12sqrt(x)

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expand (sqrt(x)(x-6)^2)/3

expand

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

\frac{x ^{2} x}{3} - 4 x x + 12 x

Solution steps

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

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

= \frac{x ( x ^{2} - 12 x + 36 )}{3}

Expand

x (x^{2} - 12 x + 36) : x^{2} x - 12 x x + 36 x

= \frac{x ^{2} x - 12 x x + 36 x}{3}

Apply the fraction rule:

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

\frac{x ^{2} x - 12 x x + 36 x}{3} = \frac{x ^{2} x}{3} - \frac{12 x x}{3} + \frac{36 x}{3}

= \frac{x ^{2} x}{3} - \frac{12 x x}{3} + \frac{36 x}{3}

Divide the numbers:

\frac{12}{3} = 4

= \frac{x ^{2} x}{3} - 4 x x + \frac{36 x}{3}

Divide the numbers:

\frac{36}{3} = 12

= \frac{x ^{2} x}{3} - 4 x x + 12 x

- \frac{2 ( 51 - 6 )}{3}

\frac{d}{d t} ((x) (- 3 x^{2} + 4))

10 e^{6 x} (3 x - 2)

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

(y + x + 2) (d x + d y + d z)

What is expand (sqrt(x)(x-6)^2)/3 ?
The solution to expand (sqrt(x)(x-6)^2)/3 is (x^2sqrt(x))/3-4xsqrt(x)+12sqrt(x)