34. Find the determinant of. b+c. a. c b. c+a. b c. c. a+b

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∣ ∣ ∣ ∣ \begin{matrix} b + c & a - b & a c + a & b - c & b a + b & c - a & c \end{matrix} ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ \begin{matrix} a - b & b - c & c - a b - c & c - a & a - b c - a & a - b & b - c \end{matrix} ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ \begin{matrix} a - b & b - c & c - a b - c & c - a & a - b c - a & a - b & b - c \end{matrix} ∣ ∣ ∣ ∣

|\begin{matrix} a - b & b + c & a \\ b - c & c + a & b \\ c - a & a + b & c \end{matrix}|

a^{3} + b^{3} + c^{3}

a^{3} + b^{3} + c^{3} - 3 a b c

∣ ∣ ∣ ∣ \begin{matrix} a - b & b - c & c - a b - c & c - a & a - b c - a & a - b & b - c \end{matrix} ∣ ∣ ∣ ∣

= 0

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