Factor 64x^3-27

Problem

64*x^3−27

Solution

1. Identify the expression as a difference of two cubes, which follows the form a^3−b^3

2. Determine the values of a and b by taking the cube root of each term.

3. Calculate a=√(3,64*x^3)=4*x

4. Calculate b=√(3,27)=3

5. Apply the formula for the difference of cubes: a^3−b^3=(a−b)*(a^2+a*b+b^2)

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

7. Simplify the terms inside the second set of parentheses: (4*x)^2=16*x^2 (4*x)*(3)=12*x and 3^2=9

Final Answer

64*x^3−27=(4*x−3)*(16*x^2+12*x+9)

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