Factor 27x^3+y^3

Problem

27*x3+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 determine the values of a and b

27*x3=(3*x)3

y3=(y)3

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

4. Substitute a=3*x and b=y into the formula.

(3*x+y)*((3*x)2−(3*x)*(y)+y2)

5. Simplify the terms within the second factor.

(3*x)2=9*x2

(3*x)*(y)=3*x*y

Final Answer

27*x3+y3=(3*x+y)*(9*x2−3*x*y+y2)

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