Factor 12c4 + 60c3 + 75c2 Completely.... Multiple choice?

12c^4 + 60c^3 + 75c62
=3c^2(4c^2+20c+25)
=3c^2{(2c)^2 +2.2c.5 +(5)^2}
=3c^2(2c+5)^2 <==ANSWER(D)
Here we apply:
a^2 +2ab +b^2 =(a+b)^2
here, a= 2c & b=5

3c² (4c² + 20c + 25)
3c² (2c + 5)(2c + 5)
3c² (2c + 5)²
OPTION D

I guess you want to factor 12 c^4 + 60 c^3 + 75 c^2
First factor out 3 c^2 to get

3 c^2 ( 4 c^2 + 20 c + 25 ) and notice that this equals
3 c^2 ( (2 c)^2 + 2 (2c) 5 + 5^2 ) the last factor being a a perfect square, namely the square of (2c +5), so the final result is

3 c^2 (2c + 5) ^2 which is D.

12c^4 + 60c^3 + 75c^2
= 3(4c^4 + 20c^3 + 25c^2)
= 3c^2(4c^2 + 20c + 25)
= 3c^2(4c^2 + 10c + 10c + 25)
= 3c^2(2c + 5)(2c + 5)
= 3c^2(2c + 5)^2
(answer D)

Only have to look at the first two components of the answers:

c2 is the highest power common factor, so A and D are ruled out.

75 is odd, so 2 isn't a factor, B is ruled out

Answer is C

12c4 + 60c3 + 75c2
=3c2(4c2 + 20c + 25)
=3c2(2c + 5)2