We can also say,
Maximum value of product of inertia = (Difference of two principal second moments of area)/2.
Polar Moment of area
We know that,
where r is the radial coordinate of a point. Note that r is independent of the inclination of the coordinate system, the sum Ixx + Iyy is independent of the inclination of the reference. This sum is also called as the polar moments of area Ip.

Second Moments and Products of Area in the rotated Coordinate System |
We observe that there is an axis system, which provides maximum value of product of area. Maximum value of product of area is equal to radius. |