Question

12 multiply the expression. (4k + 5)(3k² - 4k - 4) a 12k³ - k² - 36k - 20 b 12k³ + 31k² - 4k - 20 c 12k³ + 36k² - k - 20 d 12k³ - k² + 4k - 20

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply \(4k\) with each term in \(3k^2 - 4k - 4\) and \(5\) with each term in \(3k^2 - 4k - 4\).
\(4k(3k^2) = 12k^3\), \(4k(-4k) = -16k^2\), \(4k(-4) = -16k\)
\(5(3k^2) = 15k^2\), \(5(-4k) = -20k\), \(5(-4) = -20\)

Step2: Combine like terms

Combine the \(k^2\) terms: \(-16k^2 + 15k^2 = -k^2\)
Combine the \(k\) terms: \(-16k - 20k = -36k\)

Step3: Write the final polynomial

Combine all terms: \(12k^3 - k^2 - 36k - 20\)

Answer:

A. \(12k^3 - k^2 - 36k - 20\)