Question

Factorize the following using the Identities:
$x^2+6x+9$

Answer 1

$x^2+6x+9$
Comparing $x^2+6x+9$ with $a^2+2ab+b^2$, we see that $a=x,b=3$.
Now, $x^2+6x+9=x^2+2\left(x\right)\left(3\right)+3^2$
Using, $a^2+2ab+b^2=(a+b{)}^2,a=x$ and $b=3$,
we get $x^2+6x+9=(x+3{)}^2$.
$\therefore$ The factors of $x^2+6x+9$ are $(x+3)$ and $(x+3)$.