Factor x^3-1000

Problem

x3−1000

Solution

1. Identify the expression as a difference of two cubes, since 1000 is a perfect cube.

2. Rewrite the constant term in exponential form to clearly see the bases.

1000=10

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=10 into the formula.

(x−10)*(x2+(x)*(10)+10)

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

(x−10)*(x2+10*x+100)

Final Answer

x3−1000=(x−10)*(x2+10*x+100)

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