Problem

Multiply. (Simplify your answer completely.) \[ (2 a-4)(2 a+1)(a-2) \]

Solution

Step 1 :\((2a - 4)(2a + 1) = 2a \times 2a + 2a \times 1 - 4 \times 2a - 4 \times 1 = 4a^2 + 2a - 8a - 4 = 4a^2 - 6a - 4\)

Step 2 :\((4a^2 - 6a - 4)(a - 2) = 4a^2 \times a - 4a^2 \times 2 - 6a \times a + 6a \times 2 - 4 \times a + 4 \times 2 = 4a^3 - 8a^2 - 6a^2 + 12a - 4a + 8 = 4a^3 - 14a^2 + 8a + 8\)

Step 3 :\(\boxed{4a^3 - 14a^2 + 8a + 8}\)

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