Factor 8x^3+125

Problem

8*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

3. Calculate a by taking the cube root of 8*x3

a=2*x

4. Calculate b by taking the cube root of 125

b=5

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

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

(2*x+5)*((2*x)2−(2*x)*(5)+5)

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

(2*x+5)*(4*x2−10*x+25)

Final Answer

8*x3+125=(2*x+5)*(4*x2−10*x+25)

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