Factor 8x^3-27y^3

Problem

8*x^3−27*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 8*x^3 which is 2*x

4. Calculate b by taking the cube root of 27*y^3 which is 3*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=2*x and b=3*y into the formula.

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

Final Answer

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

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