What is expand (n-r)!(n+1-r) ?

The solution to expand (n-r)!(n+1-r) is n(n-r)!+(n-r)!-r(n-r)!

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expand (n-r)!(n+1-r)

expand

(n - r)! (n + 1 - r)

n (n - r)! + (n - r)! - r (n - r)!

Solution steps

(n - r)! (n + 1 - r)

Distribute parentheses

= (n - r)! n + (n - r)! \cdot 1 + (n - r)! (- r)

Apply minus-plus rules

+ (- a) = - a

= n (n - r)! + 1 \cdot (n - r)! - r (n - r)!

Multiply:

1 \cdot (n - r)! = (n - r)!

= n (n - r)! + (n - r)! - r (n - r)!

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

\frac{- x + 1}{5 ( x + 2 )}

2^{x (x - 1)}

\frac{2}{s ( s ^{2} + 2 s + 2 )}

\frac{( y + 1 ) ^{2}}{2}

What is expand (n-r)!(n+1-r) ?
The solution to expand (n-r)!(n+1-r) is n(n-r)!+(n-r)!-r(n-r)!