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

The solution to expand (x(x-5)^2)/2 is (x^3)/2-5x^2+(25x)/2

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

expand

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

\frac{x ^{3}}{2} - 5 x^{2} + \frac{25 x}{2}

Solution steps

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

(x - 5)^{2} = x^{2} - 10 x + 25

= \frac{x ( x ^{2} - 10 x + 25 )}{2}

Expand

x (x^{2} - 10 x + 25) : x^{3} - 10 x^{2} + 25 x

= \frac{x ^{3} - 10 x ^{2} + 25 x}{2}

Apply the fraction rule:

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

\frac{x ^{3} - 10 x ^{2} + 25 x}{2} = \frac{x ^{3}}{2} - \frac{10 x ^{2}}{2} + \frac{25 x}{2}

= \frac{x ^{3}}{2} - \frac{10 x ^{2}}{2} + \frac{25 x}{2}

Divide the numbers:

\frac{10}{2} = 5

= \frac{x ^{3}}{2} - 5 x^{2} + \frac{25 x}{2}

\frac{sin ^{2} ( θ ) + ( 1 + cos ( θ ) ) ^{2}}{cos ( θ ) + 1}

\frac{2 x ^{2} + 6 x}{( x - 3 ) ( x + 1 )}

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

- 2 (3 - 52)

\frac{12}{s ( s + 10 ) ( s + 70 )}

What is expand (x(x-5)^2)/2 ?
The solution to expand (x(x-5)^2)/2 is (x^3)/2-5x^2+(25x)/2