Factor completely:

81x4 – 81

A.

(9x2 + 9)(3x + 3)(3x – 3)

B.

(3x + 3)2(3x – 3)2

C.

(3x + 3)(3x – 3)

D.

(9x2 + 9)(9x2 – 9)

Question

Factor completely:

81x4 – 81
	
	
 
A.
	

(9x2 + 9)(3x + 3)(3x – 3)
	
 
B.
	

(3x + 3)2(3x – 3)2
	
 
C.
	

(3x + 3)(3x – 3)
	
 
D.
	

(9x2 + 9)(9x2 – 9)

anonymous · Answer

$$81x^4-81?$$

solomonzelman · Answer

$81x^4 – 81$

$81(x^4 –1 )$

$81(~(x^2)^2 –1^2 )$

$81(x^2 –1 )(x^2+1)$

and then the last step...

solomonzelman · Answer

this is how I would go about this problem, with no need to remember any identities with the 4th power.

anonymous · Answer

thanks @SolomonZelman

solomonzelman · Answer

not done yet, you need one more step to complete this problem

solomonzelman · Answer

oh, they did it differently, they didn't take 81 out....

solomonzelman · Answer

oh, typo in the rule
ok, so
81•x$^4$=3$^4$•x$^4$=(3x)$^4$

this is what you get from your initial expression:
(3x)$^4$-3$^4$

then you can factor it, using a rule
a$^4$-b$^4$=(a-b)(a+b)(a²+b²)

solomonzelman · Answer

your a is 3x
your b is 3