How do you factor 125-x^3?

Step-by-step explanation:

We have

First, 125 is a perfect cube because

and

x^3 is a perfect cube because

so we can use the difference of cubes identity

Let say we have two perfect cubes:

64 because 8×8×8=64

and 27 because 3×3×3=27 and let subtract

we know that

but using the difference of cubes identity we should get the same thing.

Remeber cube root of 64 is 4 and cube root of 27 is 3 so we have

So the difference of cubes works for real numbers. This is a good way to help remeber the identity using real numbers.

Back on to the topic,

we know that 5 is cube root of 125 and x is the cube root of x^3 so we have

First Image is the answer the second is the steps

Best of Luck

step-by-step explanation: