Evaluate
2bc+\left(c+6\right)^{2}+3b^{2}
Expand
3b^{2}+2bc+c^{2}+12c+36
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36+12c+c^{2}-2b\left(-b-c\right)+b^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-6-c\right)^{2}.
36+12c+c^{2}+2b^{2}+2bc+b^{2}
Use the distributive property to multiply -2b by -b-c.
36+12c+c^{2}+3b^{2}+2bc
Combine 2b^{2} and b^{2} to get 3b^{2}.
36+12c+c^{2}-2b\left(-b-c\right)+b^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-6-c\right)^{2}.
36+12c+c^{2}+2b^{2}+2bc+b^{2}
Use the distributive property to multiply -2b by -b-c.
36+12c+c^{2}+3b^{2}+2bc
Combine 2b^{2} and b^{2} to get 3b^{2}.
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