Question

1. $(n^2 + 6n - 4)(2n - 4)$

Explanation:

Step1: Use the distributive property (FOIL for polynomials)

Multiply each term in the first polynomial by each term in the second polynomial:
\(n^2(2n - 4) + 6n(2n - 4) - 4(2n - 4)\)

Step2: Distribute each term

For \(n^2(2n - 4)\): \(n^2\times2n - n^2\times4 = 2n^3 - 4n^2\)
For \(6n(2n - 4)\): \(6n\times2n - 6n\times4 = 12n^2 - 24n\)
For \(-4(2n - 4)\): \(-4\times2n - (-4)\times4 = -8n + 16\)

Step3: Combine like terms

Now, combine the results from Step 2:
\(2n^3 - 4n^2 + 12n^2 - 24n - 8n + 16\)
Combine the \(n^2\) terms: \(-4n^2 + 12n^2 = 8n^2\)
Combine the \(n\) terms: \(-24n - 8n = -32n\)
So we have \(2n^3 + 8n^2 - 32n + 16\)

Answer:

\(2n^3 + 8n^2 - 32n + 16\)