Answer
$(7t+3)^2$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
49t^2+42t+9
\end{array} has $ac=
49(9)=441
$ and $b=
42
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
21,21
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
49t^2+21t+21t+9
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(49t^2+21t)+(21t+9)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
7t(7t+3)+3(7t+3)
.\end{array}
Factoring the $GCF=
(7t+3)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(7t+3)(7t+3)
\\\\=
(7t+3)^2
.\end{array}
