Factor 8x^3-27

Problem

8*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=√(3,8*x^3)=2*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: (2*x)^2=4*x^2 (2*x)*(3)=6*x and 3^2=9

Final Answer

8*x^3−27=(2*x−3)*(4*x^2+6*x+9)

Want more problems? Check here!