Mathematics: Factor completely. 81x4-1 a. (3x + 1)(3x - 1)(3x + 1)(3x - 1) b. 9x? (9x2 - 1) c. (9x2 + 1)(9x2 - 1) d. (9x2 + 1)(3x + 1)(3x - 1) reset next

Factor completely. 81x4-1 a. (3x + 1)(3x - 1)(3x - id814131313559414, kalliebjones4511

yousifgorgees101

11.03.2022

Option D

(9x^2+1)(3x+1)(3x-1)

Step-by-step explanation:

We have the following expression

81x^4-1

We can rewrite the expression in the following way:

(9x^2)^2-1^2

Remember the following property

(a+b)(a-b) = a^2 -b^2

Then in this case a=(9x^2) and b=1

So we have that

(9x^2)^2-1^2

(9x^2+1)(9x^2-1)

Now we can rewrite the expression 9x^2 as follows

(3x)^2

(9x^2+1)(9x^2-1) =(9x^2+1)((3x)^2-1^2)

Then in this case a=(3x) and b=1

So we have that

(9x^2+1)(9x^2-1) =(9x^2+1)((3x)^2-1^2)

(9x^2+1)(9x^2-1) =(9x^2+1)(3x+1)(3x-1)

finally the factored expression is:

(9x^2+1)(3x+1)(3x-1)

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