Prove $\left(m-n\right)^2=m^2-2mn+n^2$(m−n)2=m2−2mn+n2.

Use the identity $\left(u+v\right)^2=u^2+2uv+v^2$(u+v)2=u2+2uv+v2 with $v<10$v<10 to find the value of $1002^2$10022.

Kathleen noticed that if she multiplies the square number $289$289 by another square number $64$64, the result is a square number.

Consider the following diagram.

Prove polynomial identities and use them to describe numerical relationships.