Answer:
[tex](5x^2-2)(25x^4 +10x^2+4)[/tex]
Step-by-step explanation:
125x^6 – 8
We write the numbers in exponential form
125= 5*5*5 = 5^3
8 = 2*2*2= 2^3
Now 125x^6 - 8 becomes 5^3x^6 - 3^3
5^3x^2*3- 3^3
[tex](5x^2)^3 - 2^3[/tex]
We got the expression in cube form a^3- b^3= (a-b)(a^2+ab+b^2)
[tex](5x^2)^3 - 2^3[/tex]
a= 5x^2 and b= 2
[tex](5x^2)^3 - 2^3=(5x^2-2)((5x^2)^2- 5x^2 * 2+ 2^2)[/tex]
=[tex](5x^2-2)(25x^4 +10x^2+4)[/tex]
