Factor x^3-729

Problem

x3−729

Solution

1. Identify the expression as a difference of two cubes, since 729 is a perfect cube.

2. Determine the cube roots of each term to find the values for the formula.

a=√(3,x3)=x

b=√(3,729)=9

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

4. Substitute a=x and b=9 into the formula.

(x−9)*(x2+(x)*(9)+9)

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

(x−9)*(x2+9*x+81)

Final Answer

x3−729=(x−9)*(x2+9*x+81)

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