Factor y^3+8

Problem

y^3+8

Solution

1. Identify the expression as a sum of two cubes, which follows the form a^3+b^3

2. Rewrite the constant term as a cube to determine the values of a and b

y^3+2^3

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

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

(y+2)*(y^2−(y)*(2)+2^2)

5. 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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