Question

Factor completely: 81x4 – 81 (9x2 + 9)(9x2 – 9) (3x + 3)2(3x – 3)2 (3x + 3)(3x – 3) (9x2 + 9)(3x + 3)(3x – 3)

Answer 1

Last voice (9x^2+9)(3x-3)(3x+3)

Answer 2

81 is the same as 3⁴.

Thus, we can write it as:
$(3x)^{4} - 3^{4}$
$= [(3x)^{2}]^{2} - [3^{2}]^{2}$
$= [(3x)^{2} - 3^{2}][(3x)^{2} + 3^{2}]$
$= (3x - 3)(3x + 3)[(3x)^{2} + 3^{2}]$
$= (3x - 3)(3x + 3)(9x^{2} + 9)$