Factor 27x^3+125

Problem

27*x3+125

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

a=√(3,27*x3)=3*x

b=√(3,125)=5

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

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

(3*x+5)*((3*x)2−(3*x)*(5)+5)

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

(3*x+5)*(9*x2−15*x+25)

Final Answer

27*x3+125=(3*x+5)*(9*x2−15*x+25)

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