#### Answer

(5x+2)(5x+2)

#### Work Step by Step

$20x+25x^{2}+4=25x^{2}+20x+4$
First, identify two numbers that multiply with each other to become 100, the product of the constant and coefficient of $x^{2}$ (4 $\times$ 25) and add together to become 20, the coefficient of x.
From inspection, we identify the numbers as 10 and 10.
Secondly split the coefficient of x into the sum of the two above numbers.
$25x^{2}+20x+4$
$=25x^{2}+(10+10)x+4$
$=25x^{2}+10x+10x+4$
Factorize by grouping to find the answer.
$25x^{2}+10x+10x+4$
$=5x(5x+2)+2(5x+2)$
$=(5x+2)(5x+2)$