Question

alguien me puede factorizar a(b^2-c^2) - bc(b-c) + a^2c - a^2b paso por paso hasta que me quede (b-c)(b-a)(a-c)?

Answer 1

$<var>a (b^{2} -c^{2} ) </var>$ -bc (b-c) + $<var>a^{2}c -a^{2}b</var>$

 

= a(b+c)(b-c) -bc (b-c) + $<var>a^{2} (c-b)</var>$

 

= a (b +c) (b-c)-bc (b-c) - $<var>a^{2}(b-c)</var>$

 

= (b-c) [a(b+c) -bc - $<var>a^{2}</var>$]

 

= (b-c)[ a(c-a) + b(a-c)]

 

= (b-c)[-a(a-c) + b(a-c)]

 

= (b-c)(a-c)(b-a)