The law of cosines says [tex] c^2 = a^2 + b^2 - 2abc\cos C [/tex].
Given this, we can add [tex] 2ab\cos C [/tex] to the both sides and subtract [tex] c^2 [/tex] from the both sides to get the equation [tex] 2ab\cos C = a^2 + b^2 - c^2 [/tex].
Thus, the value of [tex] 2ab\cos C [/tex] is [tex] \boxed{a^2 + b^2 - c^2} [/tex].
