If a + b + c = 6, ab + bc + ca =11, abc = 6 then find ( 1 – a ) ( 1 – b ) ( 1 – c ).
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bc(b+c)+ca(c+a)+ab(a+b)+3abc
=b2c+c2b+c2a+a2b+a2b+b2a+abc+abc+abc
=bc(a+b+c)+ac(a+b+c)+ab(a+b+c)
=(a+b+c)(ab+bc+ac)=6×11=6
Alternate Method : If a=1,b=2 and c=3 then,
bc(b+c)+ca(c+a)+ab(a+b)+3abc
=6×5+3×4+2×3+3×6=30+12+6+18=66.
Hope this is helpful for you.
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