Question

[(b^4)/(-2ab+a^2+b^2)]*[(a^3+2b^2-2a^2-2a^2b)/(b^3)]/[(b^2-a^2)/(ab+b^2)]因式分解····

Answer 1

[(b^4)/(-2ab+a^2+b^2)]*[(a^3+2b^2-2a^2-2a^2b)/(b^3)]/[(b^2-a^2)/(ab+b^2)]因式分解····

[(b^4)/(-2ab+a^2+b^2)]*[(a^3+2b^2-2a^2-2a^2b)/(b^3)]/[(b^2-a^2)/(ab+b^2)]

=[b^4/(b-a)^2]*[(a^3+2b^2-2a^2-2a^2b)/b^3]/[(b-a)(b+a)/b/(a+b)]
=[b^4/b^3]*[(a^3+2b^2-2a^2-2a^2b)/(b-a)^2]*[b/(b-a)]
=b^2/(b-a)^3*(a^3+2b^2-2a^2-2a^2b)

Answer 2

（AB）^ 2 +（A + B）^ 2-2A ^ 2
= A ^ 2 + B ^ 2-2AB + A ^ 2 + B ^ 2 +2 AB-2A ^ 2

= A ^ 2 + A ^ 2-2A ^ 2 + B ^ 2 + B ^ 2-2AB +2 AB

= 2B ^ 2（简化）

= 2 *（-1 / 3） ^ 2

= 2 * 1/9
= 2/9