Factor 125x^3+8y^3

Problem

125*x^3+8*y^3

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 125*x^3 which results in a=5*x

4. Calculate b by taking the cube root of 8*y^3 which results in b=2*y

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

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

7. Simplify the terms within the second factor: (5*x)^2=25*x^2 (5*x)*(2*y)=10*x*y and (2*y)^2=4*y^2

Final Answer

125*x^3+8*y^3=(5*x+2*y)*(25*x^2−10*x*y+4*y^2)

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