Factor 125x^3+64

Problem

125*x3+64

Solution

1. Identify the expression as a sum of two cubes, which follows the form a3+b3

2. Determine the cube roots of each term to find a and b

3. Calculate a by taking the cube root of 125*x3 which results in a=5*x

4. Calculate b by taking the cube root of 64 which results in b=4

5. Apply the formula for the sum of cubes: a3+b3=(a+b)*(a2−a*b+b2)

6. Substitute the values of a and b into the formula.

7. Simplify the terms inside the second factor: (5*x)2=25*x2 (5*x)*(4)=20*x and 4=16

Final Answer

125*x3+64=(5*x+4)*(25*x2−20*x+16)

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