6a^2+2b^2+3c^2+7ab+7bc+11ac
=2b^2+7b(a+c)+(6a^2+11ac+3c^2)
=2b^2+7b(a+c)+(6a^2+9ac+2ac+3c^2)
=2b^2+7b(a+c)+{3a(2a+3c)+c(2a+3c)}
=2b^2+7b(a+c)+(2a+3c)(3a+c)
=2b^2+{(4a+6c)+(3a+c)}b+(2a+3c)(3a+c)
=2b^2+(4a+6c)b+(3a+c)b+(2a+3c)(3a+c)
=2b(b+2a+3c)+(3a+c)(b+2a+3c)
=(b+2a+3c)(2b+3a+c)
By Arindam Kundu SAVM Chandannagar