find the sum, difference, or product. (Simplify your answer completely.)

Question

v³(v − 8) − 4v²(5 − 5v) (for the life of me I couldn't find a solution

Answer 1

Expand and combine similar terms: v³(v − 8) − 4v²(5 − 5v) = v⁴ - 8v³ - 20v² + 20v³ = v⁴ + 12v³ - 20v².

Answer 2

v³(v − 8) − 4v²(5 − 5v)

Multiply it out to get

v⁴ - 8v³ - 20v² + 20v³

v⁴ + 12v³ - 20v²

All terms have v² as a factor

v² * (v² + 12v - 20)

Solve the portion within the parentheses using the quadratic formula. Here a=1, b=12, c=-20.

[-b +/- sqrt(b² - 4ac)] / 2a

Plugging in values for a, b, c into the formula and solving, we get 2 solutions: -13.483315 and 1.483315

Therefore the original string boils down to two possibilities -13.483315v² and +1.483315v².