Multiply, please: (a-b)(a-b)

You can use the FOIL method:
First multiply the first terms in (a-b)(a-b):
${\displaystyle a\left(a\right)=a^2}$
Add the products of the outside and inside terms:
${\displaystyle a^2+a(-b)+a(-b)=a^2-2ab}$
Finally, add the product of the last terms:
${\displaystyle a^2-2ab+(-b)(-b)=a^2-2ab+b^2}$

You will get $=a^2-2ab+b^2$