Factor y^3-27

Problem

y3−27

Solution

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

2. Rewrite the terms as perfect cubes to find the values of a and b

y3−27=y3−3

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

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

(y−3)*(y2+(y)*(3)+3)

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

(y−3)*(y2+3*y+9)

Final Answer

y3−27=(y−3)*(y2+3*y+9)

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