Final answer:
After expanding and simplifying each pair of expressions, none of the options provided are an exact match. However, ignoring a typo in option d) allows it to make sense as equivalent expressions when simplified correctly.
Step-by-step explanation:
The student's question asks which pair shows equivalent expressions. To determine which expressions are equivalent, we must expand and simplify both sides of each equation (where applicable) and see if they result in the same expression.
For option a), we expand 2(13x + 2) to get 26x + 4, which does not equal 26x + 1. Thus, they are not equivalent.
For option b), we have an expression 2(13x + 2) on one side, and simply x + 4 on the other, which are clearly not equivalent.
For option c), both sides of the equation are different (one has x + 4 and the other x + 2), so they are not equivalent.
For option d), we can simplify 2(x + 4) - 2£x + 8. First, distribute the 2: 2x + 8. The -2£ is a typo, and if we assume it is intended to be -2x, we then have 2x + 8 - 2x + 8, which simplifies to 8 + 8, or 16. So, if we disregard the typo and the expression is 2(x + 4) - 2x + 8, it simplifies to 16 which is equivalent to two times the quantity x + 4 (2 * 8).