Factor x^3+1000

Problem

x^3+1000

Solution

1. Identify the expression as a sum of two cubes, which follows the form a^3+b^3

2. Rewrite the constant term as a cube by finding the cube root of 1000

1000=10^3

3. Apply the formula for the sum of cubes, which is a^3+b^3=(a+b)*(a^2−a*b+b^2)

4. Substitute a=x and b=10 into the formula.

(x+10)*(x^2−(x)*(10)+10^2)

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

(x+10)*(x^2−10*x+100)

Final Answer

x^3+1000=(x+10)*(x^2−10*x+100)

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