Question: Subtract 4a2 + 5b2 − 6c2 + 8 from 2a2 − 3b2 − 4c2 − 5.
Solution:
$2 a^{2}-3 b^{2}-4 c^{2}-5-\left(4 a^{2}+5 b^{2}-6 c^{2}+8\right)$
$=2 a^{2}-3 b^{2}-4 c^{2}-5-4 a^{2}-5 b^{2}+6 c^{2}-8$
$=2 a^{2}-4 a^{2}-3 b^{2}-5 b^{2}-4 c^{2}+6 c^{2}-5-8$
$=-2 a^{2}-8 b^{2}+2 c^{2}-13$
