What is expand ((k+1)(k+2)(k+3)(k+4))/4 ?

The solution to expand ((k+1)(k+2)(k+3)(k+4))/4 is (k^4)/4+(5k^3)/2+(35k^2)/4+(25k)/2+6

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expand ((k+1)(k+2)(k+3)(k+4))/4

expand

\frac{( k + 1 ) ( k + 2 ) ( k + 3 ) ( k + 4 )}{4}

\frac{k ^{4}}{4} + \frac{5 k ^{3}}{2} + \frac{35 k ^{2}}{4} + \frac{25 k}{2} + 6

Solution steps

\frac{( k + 1 ) ( k + 2 ) ( k + 3 ) ( k + 4 )}{4}

Expand

(k + 1) (k + 2) (k + 3) (k + 4) : k^{4} + 10 k^{3} + 35 k^{2} + 50 k + 24

= \frac{k ^{4} + 10 k ^{3} + 35 k ^{2} + 50 k + 24}{4}

Apply the fraction rule:

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

\frac{k ^{4} + 10 k ^{3} + 35 k ^{2} + 50 k + 24}{4} = \frac{k ^{4}}{4} + \frac{10 k ^{3}}{4} + \frac{35 k ^{2}}{4} + \frac{50 k}{4} + \frac{24}{4}

= \frac{k ^{4}}{4} + \frac{10 k ^{3}}{4} + \frac{35 k ^{2}}{4} + \frac{50 k}{4} + \frac{24}{4}

Cancel

\frac{10 k ^{3}}{4} : \frac{5 k ^{3}}{2}

= \frac{k ^{4}}{4} + \frac{5 k ^{3}}{2} + \frac{35 k ^{2}}{4} + \frac{50 k}{4} + \frac{24}{4}

Cancel

\frac{50 k}{4} : \frac{25 k}{2}

= \frac{k ^{4}}{4} + \frac{5 k ^{3}}{2} + \frac{35 k ^{2}}{4} + \frac{25 k}{2} + \frac{24}{4}

Divide the numbers:

\frac{24}{4} = 6

= \frac{k ^{4}}{4} + \frac{5 k ^{3}}{2} + \frac{35 k ^{2}}{4} + \frac{25 k}{2} + 6

(2, 5) y (- 1, - 4)

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

(x - a)^{2} + (y - b)^{2}

lo g_{10} (t^{3})

(x - e^{- x})^{2}

What is expand ((k+1)(k+2)(k+3)(k+4))/4 ?
The solution to expand ((k+1)(k+2)(k+3)(k+4))/4 is (k^4)/4+(5k^3)/2+(35k^2)/4+(25k)/2+6