Question

Simplify the polynomial expression (xy - 2)(2^2 + 1). to make a answer use the boxes
_x^3y+_x^2+_xy+_

Answer 1

To simplify the polynomial expression \((xy - 2)(2^2 + 1)\), we start by evaluating the expression in parentheses:

\[
2^2 + 1 = 4 + 1 = 5
\]

Now, substitute this back into the expression:

\[
(xy - 2)(5)
\]

Next, distribute the \(5\) across the terms inside the parentheses:

\[
5(xy - 2) = 5xy - 10
\]

Now, rewrite this in the form requested, which is \(_x^3y + _x^2 + _xy + _\).

Since there are no terms with \(x^3\), \(x^2\), or \(xy\) besides those already produced, we can fill in the boxes as follows:

- Coefficient of \(x^3y\): \(0\)
- Coefficient of \(x^2\): \(0\)
- Coefficient of \(xy\): \(5\)
- Constant term: \(-10\)

Thus, the fully simplified polynomial expression is:

\[
\boxed{0} \quad \boxed{0} \quad \boxed{5} \quad \boxed{-10}
\]