Prove - a- b - c - a-b - a-c

[ We have to prove; a ×( b + c #160; ) =( a × b #160; ) ( a × c #1 ...

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Expansion of (a ± b ± c)²

Prove : a× ...

Question

Prove : $\to a \times (\to b + \to c) = (\to a \times \to b) - (\to a \times \to c)$

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Solution

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\to a \times (\to b \times \to c) + \to b \times (\to c \times \to a) + \to c \times (\to a \times \to b) = 0

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

|\begin{matrix} a + b & b + c & c + a \\ b + c & c + a & a + b \\ c + a & a + b & b + c \end{matrix}| = 2 |\begin{matrix} a & b & c \\ b & c & a \\ c & a & b \end{matrix}|

Prove that : (i) $(A \cup B) \times C = (A \times C) \cup (B \times C)$

(ii) $(A \cap B) \times C = (A \times C) \cap (B \times C) .$

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