Question

How do you factor `3x^4-81xy^3`?

Answer 1

`3x(x-3y)(x^2+3xy+9y^2)`

Explanation:

`"take out a "color(blue)"common factor "3x`

`=3x(x^3-27y^3)`

`x^3-27y^3" is a "color(blue)"difference of cubes"`

`"which factors in general as"`

`a^3-b^3=(a-b)(a^2+ab+b^2)`

`"here "a=x" and "27y^3=(3y)^3rArrb=3y`

`x^3-27y^3=(x-3y)(x^2+3xy+9y^2)`

`3x^4-81xy^3=3x(x-3y)(x^2+3xy+9y^2)`