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This rewrite is possible due to the distributive property of multiplication over addition, specifically factoring out the common term ($k+1$). Both terms in the sum $k(k+1)$ and $2(k+1)$ share the factor ($k+1$).

Conditions: The expression is a sum of two terms: $k(k+1)$ and $2(k+1)$.; ($k+1$) is a common factor in both terms.

This rewrite is possible due to the distributive property of multiplication over addition, specifically factoring out the common term ($k+1$). Both terms in the sum $k(k+1)$ and $2(k+1)$ share the factor ($k+1$).

Conditions: The expression is a sum of two terms: $k(k+1)$ and $2(k+1)$.; ($k+1$) is a common factor in both terms.