Questions: Which pair of expressions below are equivalent? Answer 8(5k-2) and 40k-16 8k+5k and 13k^2 8(5k) and 13k k+k+k+k and k^4

Transcript text: Which pair of expressions below are equivalent? Answer $8(5 k-2)$ and $40 k-16$ $8 k+5 k$ and $13 k^{2}$ $8(5 k)$ and $13 k$ $k+k+k+k$ and $k^{4}$

Solution

Solution Steps

Step 1: Expand the first expression

Expand $ 8(5k - 2) $ using the distributive property: \[ 8(5k - 2) = 8 \cdot 5k - 8 \cdot 2 = 40k - 16. \] This matches the second expression $ 40k - 16 $, so they are equivalent.

Step 2: Simplify the second pair of expressions

Simplify $ 8k + 5k $: \[ 8k + 5k = (8 + 5)k = 13k. \] The second expression is $ 13k^2 $, which is not equal to $ 13k $. Therefore, they are not equivalent.

Step 3: Simplify the third pair of expressions

Simplify $ 8(5k) $: \[ 8(5k) = 40k. \] The second expression is $ 13k $, which is not equal to $ 40k $. Therefore, they are not equivalent.