Factor x^3+64y^3

Problem

x3+64*y3

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 x3 which is x

4. Calculate b by taking the cube root of 64*y3 which is 4*y

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

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

7. Simplify the terms within the second factor: (4*y)2=16*y2 and x*(4*y)=4*x*y

Final Answer

x3+64*y3=(x+4*y)*(x2−4*x*y+16*y2)

Want more problems? Check here!