Question

Factor completely: 81x^4 – 1

A. (9x + 1)(9x – 1)
B. (9x^2 + 1)(9x^2 – 1)
C. (3x^2 + 1)^3(3x – 1)
D. (9x^2 + 1)(3x + 1)(3x – 1)

Answer 1

`81x^4-1=\\ (9x^2)^2-1^2=\\ (9x^2+1)(9x^2-1)=\\ (9x^2+1)((3x)^2-1^2)=\\ (9x^2+1)(3x+1)(3x-1)`

Answer 2

Using this: a²-b²=(a+b)(a-b)

81x^4-1=

(9x²)²-1=

(9x²-1)(9x²+1)= (in the bold half we use the formula again)

(3x+1)(3x-1)(9x²+1)

So the answer is D