Question

What is the factored form of 125x6 – 8?

Answer 1

Answer:

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

Step-by-step 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 )

$=(5x^2+(-2)) ((5x^2)^2 - (5x^2\times -2) + (-2)^2)$

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

Which is the required factor form,

Third option is correct.

Answer 2

Hello,

Answer C

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