Answer:
[tex](5a^2-4)(25a^4 + 20a^2+16)[/tex]
Step-by-step explanation:
[tex]125a^6-64[/tex]
WE can write 125 as 5^3
Also a^6 = (a^2)^3
64 can be written as 4^3
[tex]125a^6-64[/tex]
[tex]5^3(a^2)^3-4^3[/tex]
[tex](5a^2)^3-4^3[/tex]
Now we apply a^3 - b^3 formula
[tex]a^3 - b^3 = (a-b)(a^2 + ab+b^2)[/tex]
a= 5a^2 and b = 4
Plug in the values in the formula
[tex](5a^2)^3 - (4)^3 = (5a^2-4)((5a^2)^2 + (5a^2)(4)+4^2)[/tex]
[tex] = (5a^2-4)(25a^4 + 20a^2+16)[/tex]
WE factored it completely
