The factorisation of (lm + l) + m + 1 is

(l + 1)(m + 1) (l – 1)(m – 1) (l + 1)(m – 1) (l – 1)(m + 1).

(l + 1)(m + 1)

(lm + l) + m + 1 = l ( m + 1 ) + 1 ( m + 1 ) = ( l + 1 ) . ( m + 1 )