Question

question
which pair of expressions below are equivalent?
answer
8(5k - 2) and 40k - 16
8k + 5k and 13k²
8(5k) and 13k
k + k + k + k and k⁴

Explanation:

Step1: Analyze the first pair

Using the distributive property \(a(b - c)=ab - ac\), for \(8(5k - 2)\), we have \(8\times5k-8\times2 = 40k-16\). So this pair seems equivalent. Let's check others to be sure.

Step2: Analyze the second pair

\(8k + 5k=(8 + 5)k=13k\), and \(13k^{2}\) is \(13\times k\times k\), which is not equal to \(13k\) (unless \(k = 0\) or \(k = 1\), but generally not equivalent).

Step3: Analyze the third pair

\(8(5k)=8\times5\times k = 40k\), and \(13k\) is different from \(40k\), so not equivalent.

Step4: Analyze the fourth pair

\(k + k + k + k=4k\), and \(k^{4}=k\times k\times k\times k\), which is not equal to \(4k\) (unless \(k = 0\), \(k = 1\) or \(k = 4\), but generally not equivalent).

Answer:

A. \(8(5k - 2)\) and \(40k - 16\)