Factor 8y^3-27

Problem

8*y3−27

Solution

1. Identify the expression as a difference 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

8*y3=(2*y)3

27=3

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

4. Substitute a=2*y and b=3 into the formula.

(2*y−3)*((2*y)2+(2*y)*(3)+3)

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

(2*y−3)*(4*y2+6*y+9)

Final Answer

8*y3−27=(2*y−3)*(4*y2+6*y+9)

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