EmilianaE244690 EmilianaE244690
  • 25-10-2022
  • Mathematics
contestada

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

Respuesta :

SenayaI669664 SenayaI669664
  • 25-10-2022

Given:

[tex]-2x^3-16y^3[/tex]

Aim:

We need to factorize the given polynomial.

Explanation:

Take out the common term (-2).

[tex]-2x^3-16y^3=-2(x^3+8y^3)[/tex][tex]\text{Use }8=2^3.[/tex]

[tex]-2x^3-16y^3=-2(x^3+2^3y^3)[/tex]

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

[tex]-2x^3-16y^3=-2(x+y_{})(x^2-xy+y^2)[/tex]

Final answer:

[tex]-2(x+y_{})(x^2-xy+y^2)[/tex]

Answer Link

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