Factor 8x^3-125y^3

Problem

8*x3−125*y3

Solution

1. Identify the expression as a difference 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*y3

b=5*y

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

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

(2*x−5*y)*((2*x)2+(2*x)*(5*y)+(5*y)2)

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

(2*x−5*y)*(4*x2+10*x*y+25*y2)

Final Answer

8*x3−125*y3=(2*x−5*y)*(4*x2+10*x*y+25*y2)

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