Factor 8x^3-27y^3

Problem

8*x3−27*y3

Solution

1. Identify the expression as a difference 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 8*x3 which is 2*x

4. Calculate b by taking the cube root of 27*y3 which is 3*y

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

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

7. Simplify the terms within the second factor: (2*x)2=4*x2 (2*x)*(3*y)=6*x*y and (3*y)2=9*y2

Final Answer

8*x3−27*y3=(2*x−3*y)*(4*x2+6*x*y+9*y2)

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