Questions: (n^2+6n-4)(2n-4)

Solution Steps

To solve the given problem, we need to expand and simplify the expression \((n^2 + 6n - 4)(2n - 4)\) and then compare the result with the provided options to find the correct one.

We start with the given expression: \[ (n^2 + 6n - 4)(2n - 4) \]

Next, we expand the expression using the distributive property: \[ (n^2 + 6n - 4)(2n - 4) = n^2 \cdot 2n + n^2 \cdot (-4) + 6n \cdot 2n + 6n \cdot (-4) - 4 \cdot 2n - 4 \cdot (-4) \]

Simplify each term: \[ = 2n^3 - 4n^2 + 12n^2 - 24n - 8n + 16 \]

Combine like terms: \[ = 2n^3 + 8n^2 - 32n + 16 \]

We compare the simplified expression \(2n^3 + 8n^2 - 32n + 16\) with the provided options:

1. \(2n^3 + 8n^2 - 12n + 16\)
2. \(2n^3 + 8n^2 - 32n - 16\)
3. \(2n^3 + 8n^2 - 32n + 16\)
4. \(2n^3 + 16n^2 - 32n + 16\)

The correct match is: \[ 2n^3 + 8n^2 - 32n + 16 \]

Final Answer