[tex]a (b^{2} -c^{2} ) [/tex] -bc (b-c) + [tex]a^{2}c -a^{2}b[/tex]
= a(b+c)(b-c) -bc (b-c) + [tex]a^{2} (c-b)[/tex]
= a (b +c) (b-c)-bc (b-c) - [tex]a^{2}(b-c)[/tex]
= (b-c) [a(b+c) -bc - [tex]a^{2}[/tex]]
= (b-c)[ a(c-a) + b(a-c)]
= (b-c)[-a(a-c) + b(a-c)]
= (b-c)(a-c)(b-a)
