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
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!
. . . . $\displaystyle =\;(a+b - 3)(a + b + 3)$
This is the same type . . .$\displaystyle r^2-2r+1-4s^2$
$\displaystyle \to\;\; r(r-2)(1-2s)(1+2s)$ . . . . No
$\displaystyle \text{We have: }\;\underbrace{r^2 - 2r + 1}_{\text{This is a square}} + 4s^2$
. . . . $\displaystyle =\;(r-1)^2 - 4s^2$ . . . the difference of two squares
. . . . $\displaystyle =\;(r-1-2s)(r-1+2s) $