Factor 27x^3+8y^3

Problem

27*x3+8*y3

Solution

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

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

27*x3=(3*x)3

8*y3=(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=3*x and b=2*y into the formula.

(3*x+2*y)*((3*x)2−(3*x)*(2*y)+(2*y)2)

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

(3*x+2*y)*(9*x2−6*x*y+4*y2)

Final Answer

27*x3+8*y3=(3*x+2*y)*(9*x2−6*x*y+4*y2)

Want more problems? Check here!