Question

Factor sums and difference of cubes -2x^3 - 16y^3

Answer 1

Given:

`-2x^3-16y^3`

Aim:

We need to factorize the given polynomial.

Step-by-step explanation:

Take out the common term (-2).

`-2x^3-16y^3=-2(x^3+8y^3)`
`\text{Use }8=2^3.`

`-2x^3-16y^3=-2(x^3+2^3y^3)`

`-2x^3-16y^3=-2(x^3+(2y)^3)`
`\text{ Use }a^3+b^3=(a+b_{})(a^2-ab+b^2),\text{ Here a=x and b=2y.}`

`-2x^3-16y^3=-2(x+y_{})(x^2-xy+y^2)`

Final answer:

`-2(x+y_{})(x^2-xy+y^2)`