Factor 125x^3+1

Problem

125*x3+1

Solution

1. Identify the expression as a sum 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

125*x3=(5*x)3

1=(1)3

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

4. Substitute a=5*x and b=1 into the formula.

(5*x+1)*((5*x)2−(5*x)*(1)+1)

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

(5*x+1)*(25*x2−5*x+1)

Final Answer

125*x3+1=(5*x+1)*(25*x2−5*x+1)

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