Factor 3t^3-81

Problem

3*t^3−81

Solution

1. Factor out the greatest common factor, which is 3

3*(t^3−27)

2. Identify the expression inside the parentheses as a difference of cubes, since 27=3^3

3*(t^3−3^3)

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

3*(t−3)*(t^2+3*t+3^2)

4. Simplify the constant term inside the quadratic factor.

3*(t−3)*(t^2+3*t+9)

Final Answer

3*t^3−81=3*(t−3)*(t^2+3*t+9)

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