Question

How do you completely factor 64x-x (the -x is to the power of 4)

Answer 1

Ok so the problem is 64x - x^-4
The highest common factor of the two terms is x so the answer is:

x(64 - x^3)

Now, 64 - x^3 is the 'difference of two cubes' as 64 = 4^3 so we use the formula:

X^3 - y^3 = (X - y)*(X^2 + X*y + y^2)

In our case the 'X' = '4' and
'y' = 'x'
so:
(4^3 - x^3) = (4 - x)*(4^2 + 4*x + x^2)
= (4 - x)*(16 + 4x +x^2)

So we started with:
64x - x^4
We then took 'x' out
x(64 - x^3) = x(4^3 - x^3)
and we then found out what 4^3 - x^3 was so the final answer is:

x(4 - x)(16 + 4x + x^2)

Ok, Hope that helps!