Final answer:
The term that completes the polynomial 8x³y² −_____ + 3xy²−4y³ is A. x²y², resulting in a fully simplified polynomial in standard form.
Step-by-step explanation:
The student is asking which term completes the polynomial 8x³y² −_____ + 3xy²−4y³ so that it is in standard form and fully simplified. To find the missing term, we need to look for a term that would balance the equation in terms of simplifying algebra.
Standard form means that terms should be in decreasing order of degree. Considering the polynomial starts with x³y², followed by xy², and ends with y³, we should look for a term with x²y² to maintain this order, as it has a degree of 4, which fits perfectly between the degrees of the other terms.
The correct answer is A. x²y², which completes the polynomial as 8x³y² − x²y² + 3xy²−4y³.