Factorise $25 x^{2}+25 x+6$.

(A) To factorise the quadratic expression $25 x^{2}+25 x+6$,we look for two numbers whose product is $25 \times 6 = 150$ and whose sum is $25$.
These two numbers are $15$ and $10$,since $15 \times 10 = 150$ and $15 + 10 = 25$.
Now,split the middle term $25 x$ as $15 x + 10 x$:
$25 x^{2} + 15 x + 10 x + 6$
Group the terms:
$(25 x^{2} + 15 x) + (10 x + 6)$
Factor out the common terms from each group:
$5 x(5 x + 3) + 2(5 x + 3)$
Finally,factor out the common binomial $(5 x + 3)$:
$(5 x + 3)(5 x + 2)$.