Factor 27s^3-64t^3

Problem

27*s^3−64*t^3

Solution

1. Identify the expression as a difference of two cubes, which follows the general 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*s^3() which is 3*s()

4. Calculate b by taking the cube root of 64*t^3 which is 4*t

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*s() and b=4*t into the formula.

7. Simplify the terms within the second factor: (3*s)^2=9*s^2() (3*s)*(4*t)=12*s(t) and (4*t)^2=16*t^2

Final Answer

27*s^3−64*t^3=(3*s−4*t)*(9*s^2+12*s(t)+16*t^2)

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