Can someone explain this to me. I am confused?

Question

Factor polynomial
81a^6b^4c^4 - 4d^6

Answer 1

OK... this is just a fancy-looking version of a simpler case:
x^2 - y^2 = (x+y)*(x-y)

The key is to recognize that 81a^6b^4c^4 and 4d^6 are both squares. Since there's a minus sign between them, you can use the above formula.

The square root of 81a^6b^4c^4 is 9a^3b^2c^2
The square root of 4d^6 is 2d^3

Applying what we know from above,

81a^6b^4c^4 - 4d^6 = (9a^3b^2c^2 + 2d^3) * (9a^3b^2c^2 - 2d^3)

Hope that helps!

Answer 2

81a^6b^4c^4 - 4d^6 it the difference of squares
(9a^3b^2c^2)^2-(2d^3)^2
(9a^3b^2c^2+2d^3)(9a^3b^2c^2-2d^3)

Answer 3

(9a^3b^2c^2 + 2d^3)(9a^3b^2c^2 - 2d^3)