Final answer:
The expression 4(m+p) between a²+b² seems to be algebraic manipulation with a possible typo. Assuming multiplication, the correct expansion is (4m + 4p)(a² + b²), which simplifies differently from what's provided.
Step-by-step explanation:
The student's original expression of 4(m+p) between a²+b² seems to involve algebraic manipulation but does not make complete sense with the given "entre" which could be a typo for division, multiplication, or comparison. However, if we assume the intention was multiplication, then the correct expansion would indeed be (4m + 4p)(a² + b²), which does not equal the expression provided due to an incorrect step that combines terms inappropriately.
The proper expansion would maintain the products of each term separately, giving
4(m+p) entre a²+b²
= 4m(a² + b²) + 4p(a² + b²)
= 4ma² + 4mb² + 4pa² + 4pb²