Question

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

Answer 1

Answer:

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

Step-by-step 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

Answer 2

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