What is expand ((h+1)(h+2)(2h+3))/6 ?

The solution to expand ((h+1)(h+2)(2h+3))/6 is (h^3)/3+(3h^2)/2+(13h)/6+1

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expand ((h+1)(h+2)(2h+3))/6

expand

\frac{( h + 1 ) ( h + 2 ) ( 2 h + 3 )}{6}

\frac{h ^{3}}{3} + \frac{3 h ^{2}}{2} + \frac{13 h}{6} + 1

Solution steps

\frac{( h + 1 ) ( h + 2 ) ( 2 h + 3 )}{6}

Expand

(h + 1) (h + 2) (2 h + 3) : 2 h^{3} + 9 h^{2} + 13 h + 6

= \frac{2 h ^{3} + 9 h ^{2} + 13 h + 6}{6}

Apply the fraction rule:

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

\frac{2 h ^{3} + 9 h ^{2} + 13 h + 6}{6} = \frac{2 h ^{3}}{6} + \frac{9 h ^{2}}{6} + \frac{13 h}{6} + \frac{6}{6}

= \frac{2 h ^{3}}{6} + \frac{9 h ^{2}}{6} + \frac{13 h}{6} + \frac{6}{6}

Apply rule

\frac{a}{a} = 1

\frac{6}{6} = 1

= \frac{2 h ^{3}}{6} + \frac{9 h ^{2}}{6} + \frac{13 h}{6} + 1

Cancel

\frac{2 h ^{3}}{6} : \frac{h ^{3}}{3}

= \frac{h ^{3}}{3} + \frac{9 h ^{2}}{6} + \frac{13 h}{6} + 1

Cancel

\frac{9 h ^{2}}{6} : \frac{3 h ^{2}}{2}

= \frac{h ^{3}}{3} + \frac{3 h ^{2}}{2} + \frac{13 h}{6} + 1

U (t - π)

z (a (z^{2} - a^{2}))

\frac{( x - 3 )}{x ^{2} ( x - 5 )}

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

y^{'} (x) (x)^{2} - (3 y^{2} + cos (x) y^{'} (x) + 3 y^{2} cos (x) = 0)

What is expand ((h+1)(h+2)(2h+3))/6 ?
The solution to expand ((h+1)(h+2)(2h+3))/6 is (h^3)/3+(3h^2)/2+(13h)/6+1