Factor 27x^3-8y^3

Problem

27*x^3−8*y^3

Solution

1. Identify the expression as a difference 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 27*x^3 which is 3*x

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

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

6. Substitute a=3*x and b=2*y into the formula.

7. Simplify the terms within the second factor: (3*x)^2=9*x^2 (3*x)*(2*y)=6*x*y and (2*y)^2=4*y^2

Final Answer

27*x^3−8*y^3=(3*x−2*y)*(9*x^2+6*x*y+4*y^2)

Want more problems? Check here!