Factor x^3+125

Problem

x3+125

Solution

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

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

125=5

3. Determine the variables for the formula where a=x and b=5

4. Apply the formula for the sum of cubes: a3+b3=(a+b)*(a2−a*b+b2)

(x)3+(5)3=(x+5)*(x2−(x)*(5)+5)

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

(x+5)*(x2−5*x+25)

Final Answer

x3+125=(x+5)*(x2−5*x+25)

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