Cho a+b+c=2p. Chứng minh hằng đẳng thức 2bc + b^2 + c^2

* Hướng dẫn giải

$\begin{array}{l}VP=4p\left(p-a\right)=2p.\left(2p-2a\right)\\ =\left(a+b+c\right)\left(a+b+c-2a\right)\\ =\left(a+b+c\right)\left(b+c-a\right)\\ ={\left(b+c\right)}^2-a^2\\ =2bc+b^2+c^2-a^2=VT\end{array}$

Vậy $2bc+b^2+c^2-a^2=4p\left(p-a\right)$