Question:
Find the value
$5 \sqrt{5} x^{2}+20 x+3 \sqrt{5}$
Solution:
Splitting the middle term,
$=5 \sqrt{5} x^{2}+15 x+5 x+3 \sqrt{5}$
$[\therefore 20=15+5$ and $15 \times 5=5 \sqrt{5} \times 3 \sqrt{5}]$
$=5 x(\sqrt{5} x+3)+\sqrt{5}(\sqrt{5} x+3)$
$=(\sqrt{5} x+3)(5 x+\sqrt{5})$
$\therefore 5 \sqrt{5} x^{2}+20 x+3 \sqrt{5}=(\sqrt{5} x+3)(5 x+\sqrt{5})$