1/4x^3*(-2xy^2)+(-2x^2y)*(-1/2xy)*3xyz a(a^2+ab+b^2)+b(a^2+ab+b^2)

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1/4x^3*(-2xy^2)+(-2x^2y)*(-1/2xy)*3xyz a(a^2+ab+b^2)+b(a^2+ab+b^2)
1/4x^3*(-2xy^2)+(-2x^2y)*(-1/2xy)*3xyz a(a^2+ab+b^2)+b(a^2+ab+b^2)

1/4x^3*(-2xy^2)+(-2x^2y)*(-1/2xy)*3xyz a(a^2+ab+b^2)+b(a^2+ab+b^2)
1/4x^3*(-2xy^2)+(-2x^2y)*(-1/2xy)*3xyz
=-1/2x^4y^2+3x^4y^3z
=1/2x^4y^2(6yz-1)
a(a^2+ab+b^2)+b(a^2+ab+b^2)
=a^3+a^2b+ab^2+a^2b+ab^2+b^3
=a^3+2a^b+2ab^2+b^3

1/4x^3*(-2xy^2)+(-2x^2y)*(-1/2xy)*3xyz
=-1/2x^(3+1)y^2+3x^(2+1+1)y^(1+1+1)z
=-1/2x^4y^2+3x^4y^3z
a(a^2+ab+b^2)+b(a^2+ab+b^2)
=(a+b)(a^2+ab+b^2)