Simplify the expression: 2α(α² - 4) - 3α(α² +6)

First, distribute 2α to the terms in the first parentheses:

\( 2α \cdot α² = 2α^{1+2} = 2α³ \)

\( 2α \cdot (-4) = -8α \)

So, the first part is 2α³ - 8α.

Next, distribute -3α to the terms in the second parentheses:

\( -3α \cdot α² = -3α^{1+2} = -3α³ \)

\( -3α \cdot 6 = -18α \)

So, the second part is -3α³ - 18α.

Now, combine the results:

\( (2α³ - 8α) + (-3α³ - 18α) = 2α³ - 8α - 3α³ - 18α \)

Combine like terms:

\( (2α³ - 3α³) + (-8α - 18α) = -α³ - 26α \)

Ответ: -α³ - 26α.