Factor x^3+64y^3

Problem

x^3+64*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 x^3 which is x

4. Calculate b by taking the cube root of 64*y^3 which is 4*y

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

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

7. Simplify the terms within the second factor: (4*y)^2=16*y^2 and x*(4*y)=4*x*y

Final Answer

x^3+64*y^3=(x+4*y)*(x^2−4*x*y+16*y^2)

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