Question

Factor 81-y^2

Answer 1

\[
(a+b)(a-b) = a(a+b) - b(a+b) = \\
= a^2 + ab - ab - b^2 = a^2 - b^2
\]
So..
\[
81 - y^2 = (9 + y)(9-y)
\]

Answer 2

That's quite a lot of trouble for a standard form. You are expected to know a Difference of Squares when you see one. Don't mess around with it, just factor it. They all go the same way. Not a single variation.

\(a^{2} - b^{2} = (a+b)(a-b)\) - Every time!