Question

What is the factored form of 125a^6-64

Answer 1

(5a^2-4)*(25a^4+20a^2+16) is your answer

Answer 2

`(5a^2-4)(25a^4 + 20a^2+16)`

Explanation:

`125a^6-64`

WE can write 125 as 5^3

Also a^6 = (a^2)^3

64 can be written as 4^3

`125a^6-64`

`5^3(a^2)^3-4^3`

`(5a^2)^3-4^3`

Now we apply a^3 - b^3 formula

`a^3 - b^3 = (a-b)(a^2 + ab+b^2)`

a= 5a^2 and b = 4

Plug in the values in the formula

`(5a^2)^3 - (4)^3 = (5a^2-4)((5a^2)^2 + (5a^2)(4)+4^2)`

`= (5a^2-4)(25a^4 + 20a^2+16)`

WE factored it completely