Show that [b+c c+a a+b
c+a ab b+c
a+b b++c c+a] =2[a b c
b c a
c a b]
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what was the value a, b, c,
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[ a+b b+c c+a ] = ( a+b) • [( b+c) × (c+a)]
[a b c = a • ( b × c )]
= (a + b)• [ (b×c) + ( b×a) + (c×c) + (c×a)]
:. [c×c = | c || c | sum on= 0]
=(a+b)• [ (b×c) + ( b×a ) + 0+ ( c×a) ]
= a• ( b×c) + b• (b×c) + a• (b×a) + b• (b×a) + a• ( c×a) + b• ( c× a)
= [ a,b,c] + [ b,b,c] + [ a,b,a] + [ a,c,a] + [ b,c,a]
= [ a b c ] + 0 + 0 + 0 + 0 + [ b c a ]
= [ a b c ] + [ b c a]
= [ a b c ] + [ b c a ]
= 2 [ a b c ] = R.H.S
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