Answer
$(2k+7r)^2$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
4k^2+28kr+49r^2
,$ use the factoring of trinomials in the form $ax^2+bx+c.$
$\bf{\text{Solution Details:}}$
In the trinomial expression above, $a=
4
,b=
28
,\text{ and } c=
49
.$ Using the factoring of trinomials in the form $ax^2+bx+c,$ the two numbers whose product is $ac=
4(49)=196
$ and whose sum is $b$ are $\left\{
14,14
\right\}.$ Using these two numbers to decompose the middle term results to
\begin{array}{l}\require{cancel}
4k^2+14kr+14kr+49r^2
.\end{array}
Using factoring by grouping, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(4k^2+14kr)+(14kr+49r^2)
\\\\=
2k(2k+7r)+7r(2k+7r)
\\\\=
(2k+7r)(2k+7r)
\\\\=
(2k+7r)^2
.\end{array}
