1. factoring ?

I keep getting stuck plz help

a^2+2ab+b^2-9

->a(a+2b)(b^2-9)
->a(a+2b)(b+3)(b-3)

but the answer is -> (a+b+3) (a+b-3)

second question

r^2-2r+1-4s^2

->r(r-2)(1-2s)(1+2s)

but the answer is -> (r-1+2s)(r-1-2s)

any help will be appreciated

2. Hello, onymousillusion!

You are making some serious errors . . .

$\displaystyle a^2+2ab+b^2-9$

$\displaystyle \to \;\;a(a+2b)(b^2-9)$ . . . . No

$\displaystyle \text{We have: }\;\underbrace{a^2 + 2ab + b^2}_{\text{This is a sqsuare}} \,-\, 9$

. . . . $\displaystyle =\;(a+b)^2 - 9$ . . . This is the difference of two squares!

. . . . $\displaystyle =\;(a+b - 3)(a + b + 3)$

$\displaystyle r^2-2r+1-4s^2$

$\displaystyle \to\;\; r(r-2)(1-2s)(1+2s)$ . . . . No
This is the same type . . .

$\displaystyle \text{We have: }\;\underbrace{r^2 - 2r + 1}_{\text{This is a square}} + 4s^2$

. . . . $\displaystyle =\;(r-1)^2 - 4s^2$ . . . the difference of two squares

. . . . $\displaystyle =\;(r-1-2s)(r-1+2s)$

3. thanks for the help..... Them difference of squares are killing me when there more then 2 terms... but thanks again for the help