Math

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Factor:
3cd²(c+d)-a³c+d³(d+c)+b³d-3ab²c+3c²d(c+d)+3a²bc-3a²bd-a³d+3ab²d+b³c+c³(c+d).

[shyamjayakannan]

[tex]3cd^2(c+d)-a^3c+d^3(d+c)+b^3d-3ab^2c+3c^2d(c+d)+3a^2bc-3a^2bd-a^3d+3ab^2d+b^3c+c^3(c+d)[/tex]
[tex]=(c+d)\left(c^3+d^3+3c^2d+3d^2c\right)+c\left(b^3-a^3+3a^2b-3b^2a\right)+d\left(b^3-a^3-3a^2b+3b^2a\right)[/tex]
[tex]=(c+d)(c+d)^3+c(b-a)^3+d\left\{(b-a)^3-6a^2b+6b^2a\right\}[/tex]
[tex]=(c+d)^4+(c+d)(b-a)^3+6abd(b-a)[/tex]
[tex]=\boxed{(c+d)\left\{(c+d)^3+(b-a)^3\right\}+6abd(b-a)}[/tex]