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:

Side 1 = a

Side 2 = b

Side 3 = c

a = 2b

c = 5ft. + b

a + b + c = 49 feet

Substitute

2b + b + 5ft + b = 49 ft

Add the b’s

4b + 5ft = 49ft

Subtract 5ft from both sides of the equation

4b = 44ft

Divide both sides of the equation by 4 to isolate b

b = 11ft

a = b * 2 = 11 * 2 = 22ft

c = 49ft - 11ft - 22ft = 16ft

Hope this helps :)