Chapter 8, Problem 30CT

To determine

To Find :The missing value in each perfect square-trinomial.

Answer to Problem 30CT

The polynomial is $\left(n+9\right)\left(n+9\right)$ .

Explanation of Solution

Given information:

Consider the polynomial is $n²+\square n+81$ .

From the given equation

  $a=1,b=?$ and $c=81$ .

The product of the $ac=81$ , and sum of the 9 and 9 is 18 and it's product is 81 that's why the middle term is 18.

Put the value of the middle term in given expression

  $\begin{array}{l}n²+NAn+81=n²+18n+81\\ =n²+9n+9n+81 \left(\text{write the middle term as }18n=9n+9n\right)\\ =n\left(n+9\right)+9\left(n+9\right) \left(\text{Factor out the GCF of each group }oftwoterms\right)\\ =\left(n+9\right)\left(n+9\right) \left(\text{Factor out the common factor }n+9\right)\end{array}$

Therefore, the polynomial is:- $\left(n+9\right)\left(n+9\right)$ .