Question

5c^4-3125
is it (c-25)^4 If I am factoring

Answer 1

No wait it would be 5(c-25)^4

Answer 2

No, it is neither. \[5c^4-3125 = 5(c^4-625)\]
But now we can do something useful with this... Note that 5^4 = 625 so:

\[5(c^4-625) = 5(c^4-(5)^4)\]

And this is the difference of squares because

\[(c^2)^2 = c^4\]

So let's use the difference of squares now:

\[5(c^4-5^4)= 5(c^2-5^2)(c^2+5^2)\]

and again... to give us the final answer!

\[5c^4-3125=5(c-5)(c+5)(c^2-5^2)\]

Answer 3

Thank you I get baffled with this factoring stuff.