a) a(b2 + c2) + b(a2 + c2) + c(a2 + b2) + 2abc = ab2 + ac2 + bc2 + ba2 + a2c + b2c + abc + abc = (ab2 + b2c) + ( ac2 + a2c) + ( bc2 + abc) + ( ba2 + abc) = b2 ( a + c) + ac ( a + c) + bc ( c + a) + ba ( a + c) = ( a + c ) (b2 + ac + bc + ba) = ( a + c ) (( b2+ bc ) + ( ac + ba )) = ( a + c ) ( b( b+c) + a ( c + a)) = ( a + c ) ( b+ c ) (b + a)
b) abc - ( ab + bc + ca ) + (a + b + c) -1 = abc - ab - bc - ca + a + b + c -1 = ( abc - ab ) - (bc - b) - (ac - a) + ( c -1) = ab( c - 1) - b ( c - 1) - a( c - 1) + ( c -1) = ( c -1)(ab - b - a +1) = ( c -1)( (ab -b ) - ( a -1)) = ( c -1)( b( a -1) - ( a -1)) = ( c -1)( a -1)(b -1)