Question

1 multiple choice 1 point what is a simpler form of the expression? (2k + 4)(2k² - 5k - 4) a) 4k³ + 18k² - 12k - 16 c) 4k³ - 2k² + 12k - 16 b) 4k³ + 28k² - 2k - 16 d) 4k³ - 2k² - 28k - 16 a b c d clear my selection

Explanation:

a mistake in the problem or the selection. However, based on the correct multiplication, the answer should be D. But let's check the options again:

A) \(4k^3 + 18k^2 - 12k - 16\)
B) \(4k^3 + 28k^2 - 2k - 16\)
C) \(4k^3 - 2k^2 + 12k - 16\)
D) \(4k^3 - 2k^2 - 28k - 16\)

Wait, maybe the original expression is \((2k + 4)(2k^2 + 5k - 4)\):

\(2k \times 2k^2 = 4k^3\)
\(2k \times 5k = 10k^2\)
\(2k \times (-4) = -8k\)
\(4 \times 2k^2 = 8k^2\)
\(4 \times 5k = 20k\)
\(4 \times (-4) = -16\)

Combine \(k^2\): \(10k^2 + 8k^2 = 18k^2\)
Combine \(k\): \(-8k + 20k = 12k\)
So \(4k^3 + 18k^2 + 12k - 16\) (not an option).

Alternatively, if the expression is \((2k - 4)(2k^2 + 5k - 4)\):

\(2k \times 2k^2 = 4k^3\)
\(2k \times 5k = 10k^2\)
\(2k \times (-4) = -8k\)
\(-4 \times 2k^2 = -8k^2\)
\(-4 \times 5k = -20k\)
\(-4 \times (-4) = 16\)

Combine \(k^2\): \(10k^2 - 8k^2 = 2k^2\) (no)

Wait, maybe the original expression is \((2k + 4)(2k^2 - 5k + 4)\):

\(2k \times 2k^2 = 4k^3\)
\(2k \times (-5k) = -10k^2\)
\(2k \times 4 = 8k\)
\(4 \times 2k^2 = 8k^2\)
\(4 \times (-5k) = -20k\)
\(4 \times 4 = 16\)

Combine \(k^2\): \(-10k^2 + 8k^2 = -2k^2\)
Combine \(k\): \(8k - 20k = -12k\)
Constant: \(16\) (not \(-16\))

This is confusing. But based on the given expression \((2k + 4)(2k^2 - 5k - 4)\), the correct simplification is \(4k^3 - 2k^2 - 28k - 16\), which is option D. However, the selected option in the image is C, which suggests a possible error in the problem or the selection. But following the mathematical steps, the correct answer is D.

Answer:

D. \(4k^3 - 2k^2 - 28k - 16\)