Another algebra problem?

Question

(3c^4-3d^4)/(-6c^2+6d^2)
simplify
and please explain

Answer 1

(3c^4-3d^4)/(-6c^2+6d^2)

= (c^4 - d^4)/(2d^2 - 2c^2)

= (c^4 - d^4)/[2(d^2 - c^2)]

= [(c-d)(c+d)(c^2 + d^2)] / [-2(c+d)(c-d)]

= -(c^2 + d^2)/2

Answer 2

First, factor out what you can:

(3c^4 - 3d^4) / (-6c^2 + 6d^2)
3(c^4 - d^4) / 6(-c^2 + d^2)
3(c^4 - d^4) / -6(c^2 - d^2)
(c^4 - d^4) / -2(c^2 - d^2)

Remember that a^2 - b^2 = (a+b)(a-b), so on the top we have:

(c^2 - d^2)(c^2 + d^2) / -2(c^2 - d^2)

Terms cancel and we have
(-1/2)(c^2 + d^2)

Answer 3

= 3.(c² - d²).(c² + d²) / (-6).(c² - d²)
= (-1/2).(c² + d²)

Answer 4

factor out the 3 and -6 3(c^4-d^4)/-6(c^2-d^2)

factor the c^4-d^4

3(c^2+d^2)(c^2-d^2)/-6(c^2-d^2)

cancel stuff!!

-(c^2+d^2)/2