Which term could be put in the blank to create a fully simplified polynomial written in standard for \( 8 x^{3} y^{2}- \) \( x^{2} y^{2} \) \( x^{3} y^{3} \) \( 7 x y^{2} \) \( 7 x^{0} y^{3} \)

To create a fully simplified polynomial written in standard form, we need to combine the given terms. The standard form of a polynomial is typically written in descending order of the degree of the terms. Let's first identify the degrees of each term: 1. \( 8x^3y^2 \) has a degree of \( 3 + 2 = 5 \). 2. \( -x^2y^2 \) has a degree of \( 2 + 2 = 4 \). 3. \( x^3y^3 \) has a degree of \( 3 + 3 = 6 \). 4. \( -7xy^2 \) has a degree of \( 1 + 2 = 3 \). 5. \( 7x^0y^3 \) (which is \( 7y^3 \)) has a degree of \( 0 + 3 = 3 \). Now, let's combine these terms. The polynomial will be simplified by adding or subtracting the coefficients of like terms. To find a term that could be added to create a fully simplified polynomial, we can consider the highest degree term, which is \( x^3y^3 \) (degree 6). If we want to keep the polynomial in standard form, we can add a term that has a degree of 6 or lower. The term \( x^3y^3 \) is already present, so we can add or subtract coefficients from the other terms. If we want to ensure that the polynomial is fully simplified, we can add a term that would allow us to combine with \( x^3y^3 \). For example, if we add \( -x^3y^3 \), we would have: \[ 8x^3y^2 - x^2y^2 + x^3y^3 - 7xy^2 + 7y^3 - x^3y^3 \] This would simplify to: \[ 8x^3y^2 - x^2y^2 - 7xy^2 + 7y^3 \] However, if we want to keep the polynomial in standard form, we can simply add \( 0 \) (which is \( 0x^3y^3 \)) to keep the polynomial unchanged. Thus, the term that could be put in the blank to create a fully simplified polynomial written in standard form is: \[ 0 \] This keeps the polynomial unchanged and allows it to remain in standard form.