Question

Factor for the following expression.


49y6-42y3+9

Answer 1

`Method\ 1:\\\\49y^6=7^2y^(3\cdot2)=(7y^3)^2\\\\42y^3=2(7y^3)(3)\\\\9=3^2\\\\49y^6-42y^3+9=(7y^3)^2-2(7y^3)(3)+3^2\\\\\text{Use}\ (a-b)^2=a^2-2ab+b^2\\\\=(7y^3-3)^2=\boxed{(7y^3-3)(7y^3-3)}\\---------------------------`

`Method\ 2:\\\\49y^6-42y^3+9=49y^6-21y^3-21y^3+9=7y^3(7y^3-3)-3(7y^3-3)\\\\=\boxed{(7y^3-3)(7y^3-3)}`