\(A=2a^2b^2+2b^2c^2+2a^2c^2-a^4-b^4-c^4\)
\(A=4a^2b^2-\left(2a^2b^2-2b^2c^2-2a^2c^2+a^4+b^4+c^4\right)\)
\(A=\left(2ab\right)^2-\left(a^2+b^2-c^2\right)^2\)
\(A=\left(2ab+a^2+b^2-c^2\right)\left(2ab-a^2-b^2+c^2\right)\)
\(A=\left[\left(a+b\right)^2-c^2\right]\left[c^2-\left(a-b\right)^2\right]\)
\(A=\left(a+b+c\right)\left(a+b-c\right)\left(c+a-b\right)\left(c-a+b\right)\)
Do \(a,b,c\) là 3 cạnh của tam giác nên:
\(a+b+c>0\) ; \(a+b-c>0\) ; \(c+a-b>0\) ; \(c-a+b>0\)
Do đó: \(A>0\)
A=2a2b2+2b2c2+2a2c2−a4−b4−c4A=2a2b2+2b2c2+2a2c2−a4−b4−c4
A=4a2b2−(2a2b2−2b2c2−2a2c2+a4+b4+c4)A=4a2b2−(2a2b2−2b2c2−2a2c2+a4+b4+c4)
A=(2ab)2−(a2+b2−c2)2A=(2ab)2−(a2+b2−c2)2
A=(2ab+a2+b2−c2)(2ab−a2−b2+c2)A=(2ab+a2+b2−c2)(2ab−a2−b2+c2)
A=[(a+b)2−c2][c2−(a−b)2]A=[(a+b)2−c2][c2−(a−b)2]
A=(a+b+c)(a+b−c)(c+a−b)(c−a+b)
