Question

factorizar.
w^2 + 18w + 81

Explanation:

Step1: Recognize the perfect - square trinomial form

The general form of a perfect - square trinomial is $a^{2}+2ab + b^{2}=(a + b)^{2}$. In the given expression $w^{2}+18w + 81$, we have $a = w$ since $a^{2}=w^{2}$, and $2ab=18w$. If $a = w$, then $2wb=18w$, so $b = 9$ (because when we solve $2wb=18w$ for $b$, we divide both sides by $2w$ ($w
eq0$), and also $b^{2}=81$).

Step2: Factor the trinomial

Using the perfect - square trinomial formula $a^{2}+2ab + b^{2}=(a + b)^{2}$, substituting $a = w$ and $b = 9$, we get $(w + 9)^{2}$.

Answer:

$(w + 9)^{2}$