Factor 8x^3-27

Problem

8*x3−27

Solution

1. Identify the expression as a difference of two cubes, which follows the form a3−b3

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

3. Calculate a=√(3,8*x3)=2*x

4. Calculate b=√(3,27)=3

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 inside the second set of parentheses: (2*x)2=4*x2 (2*x)*(3)=6*x and 3=9

Final Answer

8*x3−27=(2*x−3)*(4*x2+6*x+9)

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