Factor 64x^3+125

Problem

64*x^3+125

Solution

1. Identify the expression as a sum of two cubes, which follows the form a^3+b^3

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

3. Calculate a by taking the cube root of 64*x^3 which is 4*x

4. Calculate b by taking the cube root of 125 which is 5

5. Apply the formula for the sum of cubes: a^3+b^3=(a+b)*(a^2−a*b+b^2)

6. Substitute a=4*x and b=5 into the formula.

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

Final Answer

64*x^3+125=(4*x+5)*(16*x^2−20*x+25)

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