Prove that $\left(m-n\right)^2=m^2-2mn+n^2$(m−n)2=m2−2mn+n2, showing all steps of work.
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. For example, the difference of two squares; the sum and difference of two cubes; the polynomial identity (x^2 + y^2 )^2 = (x^2 – y^2 )^2 + (2xy)^2 can be used to generate Pythagorean triples