Factor y^3-8

Problem

y^3−8

Solution

1. Identify the expression as a difference of two cubes by rewriting the constant term as a power of 3

y^3−2^3

2. Apply the formula for the difference of cubes, which states a^3−b^3=(a−b)*(a^2+a*b+b^2)

Let *a=y* and *b=2

3. Substitute the values of a and b into the factoring pattern.

(y−2)*(y^2+(y)*(2)+2^2)

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

(y−2)*(y^2+2*y+4)

Final Answer

y^3−8=(y−2)*(y^2+2*y+4)

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