What is expand (k^2+k)*(k+1)! ?

The solution to expand (k^2+k)*(k+1)! is k^2(k+1)!+k(k+1)!

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expand (k^2+k)*(k+1)!

expand

(k^{2} + k) \cdot (k + 1)!

k^{2} (k + 1)! + k (k + 1)!

Solution steps

(k^{2} + k) (k + 1)!

= (k + 1)! (k^{2} + k)

Apply the distributive law:

a (b + c) = ab + a c

a = (k + 1)!, b = k^{2}, c = k

= (k + 1)! k^{2} + (k + 1)! k

= k^{2} (k + 1)! + k (k + 1)!

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e^{t} (cos (4 t) - 2 sin (4 t))

What is expand (k^2+k)*(k+1)! ?
The solution to expand (k^2+k)*(k+1)! is k^2(k+1)!+k(k+1)!