Factor 27x^3-64y^3

Problem

27*x3−64*y3

Solution

1. Identify the expression as a difference of two cubes, which follows the general 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 27*x3 which results in a=3*x

4. Calculate b by taking the cube root of 64*y3 which results in b=4*y

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

6. Substitute the values of a and b into the formula.

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

Final Answer

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

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