What is expand (w(L-x)^3)/(3L) ?

The solution to expand (w(L-x)^3)/(3L) is (wL^2)/3-wLx+wx^2-(wx^3)/(3L)

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expand (w(L-x)^3)/(3L)

expand

\frac{w ( L - x ) ^{3}}{3 L}

\frac{w L ^{2}}{3} - w Lx + w x^{2} - \frac{w x ^{3}}{3 L}

Solution steps

\frac{w ( L - x ) ^{3}}{3 L}

(L - x)^{3} = L^{3} - 3 L^{2} x + 3 L x^{2} - x^{3}

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

Expand

w (L^{3} - 3 L^{2} x + 3 L x^{2} - x^{3}) : w L^{3} - 3 w L^{2} x + 3 w L x^{2} - w x^{3}

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

Apply the fraction rule:

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

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

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

Cancel

\frac{w L ^{3}}{3 L} : \frac{w L ^{2}}{3}

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

Cancel

\frac{3 w L ^{2} x}{3 L} : w Lx

= \frac{w L ^{2}}{3} - w Lx + \frac{3 w L x ^{2}}{3 L} - \frac{w x ^{3}}{3 L}

Cancel

\frac{3 w L x ^{2}}{3 L} : w x^{2}

= \frac{w L ^{2}}{3} - w Lx + w x^{2} - \frac{w x ^{3}}{3 L}

v (- 8, 3) d (x = - 10.5)

\frac{π ( 82 82 - 1 )}{9}

\frac{( 2 s ^{2} + 5 s )}{( ( s ^{2} + 4 ) ( s ^{2} + 1 ) )}

- 2 (arctan (3 x) - arctan (2 x)) + x

x + x

What is expand (w(L-x)^3)/(3L) ?
The solution to expand (w(L-x)^3)/(3L) is (wL^2)/3-wLx+wx^2-(wx^3)/(3L)