Factor 64x^3-27y^3

Problem

64*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 64*x3 which is 4*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=4*x and b=3*y into the formula.

7. Simplify the terms inside the second factor: (4*x)2=16*x2 (4*x)*(3*y)=12*x*y and (3*y)2=9*y2

Final Answer

64*x3−27*y3=(4*x−3*y)*(16*x2+12*x*y+9*y2)

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