How to factor $a^2-2a$

Question

The part of the problem I'm doing has me factoring this: $a^2-2a$ and I'm at a loss on how to factor it. Would I be right in saying:

$(a-1)^2$

Okay so I just ran across this part now: $a^4-16$ I'm pretty bad at factoring and my teacher neglected to teach how to do this so I'm in the process of trying to figure stuff out for myself lol.

Would I need to take the square root of $a^4$ and $16$ to get $a^2 -4$ and then factor from there?

Answer 1

Both terms contain a factor of $a$: $$a^2 - 2a = \color{red}{a}\cdot \color{blue}{a} - \color{red}{2}\cdot \color{blue}{a} = (\color{red}{a - 2})\color{blue}{a} = a(a-2){}{}{}{}{}{}$$

Compare $a^2 - 2a$ to $(a - 1)^2 = a^2 - 2a + 1$.

Answer 2

No it would not be right since $(a-1)^2 = (a-1)(a-1) = a^2-a-a+1 = a^2-2a+1$.