Question 34: Polynomial analysis \(\begin{aligned} &(a+b+c)^{2}+(a+bc)^{2}-4 c^{2} \end{aligned}\ ) to multiply:

\(\begin{aligned} &(a+b+c)^{2}+(a+bc)^{2}-4 c^{2} \\ &=(a+b+c)^{2 }+(a+bc-2 c)(a+b-c+2 c) \\ &=(a+b+c)^{2}+(a+b-3 c)(a+b+c ) \\ &=(a+b+c)(a+b+c+a+b-3 c) \\ &=(a+b+c)(2 a+2 b-2 c) \\ & =2(a+b+c)(a+bc) \end{aligned}\)