Question

How do you factor `8x^3*y^6 + 27`?

Answer 1

`(2xy^2+3)(4x^2y^4-6xy^2+9)`

Explanation:

Sum of cubes: `(a^3+b^3)=(a+b)(a^2-ab+b^2)`

Since `8x^3y^6+27=(2xy^2)^3+(3)^3`,

`a=2xy^2`
`b=3`

`8x^3y^6+27=(2xy^2+3)(4x^2y^4-6xy^2+9)`