SOLUTION: How do I factor this? 4(z-4)^2-16 Thanks!

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Question 676189: How do I factor this? 4(z-4)^2-16 Thanks!
Found 2 solutions by jim_thompson5910, lwsshak3:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use the difference of squares rule.

4(z-4)^2-16

(2(z-4))^2-(4)^2

(2(z-4)-4)(2(z-4)+4)

(2z-8-4)(2z-8+4)

(2z-12)(2z-4)

(2(z-6)(2(z-2))

(2*2)(z-6)(z-2)

4(z-6)(z-2)

So 4(z-4)^2-16 fully factors to 4(z-6)(z-2)

Note: optionally, you can expand out the original expression and factor another way, but this way seems more direct in my opinion.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
How do I factor this? 4(z-4)^2-16
this is a difference of 2 squares: (a^2-b^2)=(a+b)(a-b)
4(z-4)^2-16=(2(z-4)+4)(2(z-4)-4)
=(2z-8+4)(2z-8-4)
=(2z-4)(2z-12)
=2(z-2)2(z-6)
=4(z-2)(z-6)