Factor 8x^3-1

Problem

8*x3−1

Solution

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

2. Rewrite each term as a perfect cube to find the values of a and b

8*x3=(2*x)3

1=1

3. Apply the formula for the difference of cubes, which is a3−b3=(a−b)*(a2+a*b+b2)

4. Substitute a=2*x and b=1 into the formula.

(2*x−1)*((2*x)2+(2*x)*(1)+1)

5. Simplify the terms inside the second set of parentheses.

(2*x−1)*(4*x2+2*x+1)

Final Answer

8*x3−1=(2*x−1)*(4*x2+2*x+1)

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