Is this the correct way?
\(\displaystyle AC^2 D+2ABCD+A^2 BC>BCD^2+B^2 D^2+AB^2 D+A^2 C^2\)
\(\displaystyle (AC-BD)(AB-AC+BD+CD)>0\)
greater that 0 when \(\displaystyle (AC-BD)>0\ \ and\ \ (AB-AC+BD+CD)>0\)
and when \(\displaystyle (AC-BD)<0\ \ and\ \ (AB-AC+BD+CD)<0\)
\(\displaystyle so\ \ AC^2 D+2ABCD+A^2 BC>BCD^2+B^2 D^2+AB^2 D+A^2 C^2\)
\(\displaystyle when\ \ AC>BD\ \ and\ \ AB+CD>AC-BD\)
\(\displaystyle or\ \ AC<BD\ \ and\ \ AB+CD<AC-BD\)
Is there anything else I should be doing with this or a 'correct' way of presenting it?
Thanks
\(\displaystyle AC^2 D+2ABCD+A^2 BC>BCD^2+B^2 D^2+AB^2 D+A^2 C^2\)
\(\displaystyle (AC-BD)(AB-AC+BD+CD)>0\)
greater that 0 when \(\displaystyle (AC-BD)>0\ \ and\ \ (AB-AC+BD+CD)>0\)
and when \(\displaystyle (AC-BD)<0\ \ and\ \ (AB-AC+BD+CD)<0\)
\(\displaystyle so\ \ AC^2 D+2ABCD+A^2 BC>BCD^2+B^2 D^2+AB^2 D+A^2 C^2\)
\(\displaystyle when\ \ AC>BD\ \ and\ \ AB+CD>AC-BD\)
\(\displaystyle or\ \ AC<BD\ \ and\ \ AB+CD<AC-BD\)
Is there anything else I should be doing with this or a 'correct' way of presenting it?
Thanks