Factor x^3-8y^3

Problem

x3−8*y3

Solution

1. Identify the expression as a difference of two cubes.

2. Rewrite the terms as perfect cubes to identify the bases.

x3−(2*y)3

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

4. Substitute a=x and b=2*y into the formula.

(x−2*y)*(x2+x*(2*y)+(2*y)2)

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

(x−2*y)*(x2+2*x*y+4*y2)

Final Answer

x3−8*y3=(x−2*y)*(x2+2*x*y+4*y2)

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