Factor 125x^3+27

Problem

125*x3+27

Solution

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

2. Determine the cube roots of each term to find a and b

3. Calculate a by taking the cube root of 125*x3

a=√(3,125*x3)=5*x

4. Calculate b by taking the cube root of 27

b=√(3,27)=3

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

6. Substitute the values of a and b into the formula.

(5*x+3)*((5*x)2−(5*x)*(3)+3)

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

(5*x+3)*(25*x2−15*x+9)

Final Answer

125*x3+27=(5*x+3)*(25*x2−15*x+9)

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