Check the identity $(a+b{)}^2=a^2+2ab+b^2$ for $a=6$ and $b=4$. What value does each side give?

Identities save time and reveal structure. Examples of clever uses:

- Compute $102^2$ mentally: $(100+2{)}^2=100^2+2(100)(2)+2^2=10000+400+4=10404$.
- Compute $99\times 101:(100-1)(100+1)=100^2-1^2=10000-1=9999$.
- Compute $47^2-43^2:(47-43)(47+43)=4\times 90=360$.

Look at any number-pair calculation; if you can rewrite it as one of the three identity forms, the answer falls out.