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Simplify -3y(y²-2y+4)​

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Answer:

Explanation:

The only way in which you can truly simplify this is to factor the quantity within parentheses. Use the quadratic formula for this purpose:

y^2 - 2y + 4 has coefficients {1, -2, 4}. The discriminant is b^2 - 4ac, which here is (-2)^2 - 4(1)(4), or 4 - 16, or -12. Since the discriminant is negative, we know that the roots of this quadratic are complex, different:

-b ± i√(discriminant)

y = ---------------------------------

2a

-(-2) ±i√12 2 ±i2√3)

Then y = ------------------- = ---------------- = 1 ±i√3

2 2

and we end up with these three factors: x, x - 1 +i√3, x - 1 -i√3

So the original expression becomes -3·y·(y-1i√3)(y - 1 -i√3)

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