Question

What is the factored form of 125x6 – 8?

(5x2 – 2)(25x4 – 10x2 – 4)
(5x2 – 2)(25x4 – 10x2 + 4)
(5x2 – 2)(25x4 + 10x2 + 4)
(5x2 – 2)(25x4 + 10x2 – 4)

Answer 1

Hello,

Answer C

125x^6-8=(5x²)^3-2^3=(5x²-3)((5x²)²+2*5*x²+4)

Answer 2

`(5x^2-2)(25x^4+10x^2+4)`

Explanation:

Given expression,

`125x^6-8`

`=(5)^3 (x^2)^3 -2^3`
`\because (ab)^m=a^mb^m\text{ and }a^(mn)=(a^m)^n`

`=(5x^2)^3+(-2)^3`

By using a³ + b³ = (a-b) (a² -ab + b² )

`=(5x^2+(-2)) ((5x^2)^2 - (5x^2* -2) + (-2)^2)`

`=(5x^2-2)(25x^4+10x^2+4)`

Which is the required factor form,

Third option is correct.