Express $(x + y)^2$ in terms of $x^2$, $y^2$, and $xy$. Then plug in the given values for $x + y$ and $x^2 + y^2$ to form an equation with $xy$ as the only unknown.

Once you have an equation like a number equals $10 + 2xy$, rearrange it by subtracting and dividing so that $xy$ is alone on one side.

In Desmos, enter the equations x^2 + y^2 = 10 and x + y = 4. Desmos will graph a circle and a line and show their intersection points.

Click (or tap) on each intersection point to see its coordinates $(x, y)$. You should see two points; note the $x$ and $y$ values for either point.

In a new expression line, type the product of the $x$ and $y$ coordinates of one intersection point (for example, if a point is $(a, b)$, type a*b). The numerical output shown by Desmos is the value of $xy$ that answers the question.

Notice that you are given $x^2 + y^2$ and $x + y$, but you are asked for $xy$.

Use the algebraic identity:

This connects all three quantities in one equation.

You are told that $x + y = 4$, so

You are also told that $x^2 + y^2 = 10$, so substitute into the identity:

Now you have a simple linear equation in terms of $xy$.

From

subtract 10 from both sides:

Divide both sides by 2:

So, the value of $xy$ is $3$, which corresponds to choice B.