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

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

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

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Apply rule

\frac{a}{a} = 1

\frac{6}{6} = 1

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

Cancel

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

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

Cancel

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

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

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

(sec (x) +, - 1) (sec (x) -, + 1)

\frac{x ^{4} ( 16 x ^{2} y ^{6} + 3 ) ^{2}}{16}

\frac{d}{d t} ((z (t, x, y)) (x^{2} + y^{2}))

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