Factor y^3-125

Problem

y3−125

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

y3−5

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=5 into the formula.

(y−5)*(y2+(y)*(5)+5)

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

(y−5)*(y2+5*y+25)

Final Answer

y3−125=(y−5)*(y2+5*y+25)

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