Factor x^3+8y^3

Problem

x3+8*y3

Solution

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

2. Rewrite each term as a perfect cube to find the values of a and b

x3+8*y3=(x)3+(2*y)3

3. Apply the formula for the sum 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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