Question

Factorize the following trinomial:
$2{(m+2n)}^2+5(m+2n)+2$

Answer 1

To factorise: $2(m+2n{)}^2+5(m+2n)+2$

Now, let $(m+2n)=x$

So,

$2(m+2n{)}^2+5(m+2n)+2$

$=2x^2+5x+2$

$=2x^2+4x+x+2$

$=2x(x+2)+1(x+2)$

$=(2x+1)(x+2)$

Putting the value of $x$

$=\left[2\right(m+2n)+1]\left[\right(m+2n)+2]$

$=(2m+4n+1)(m+2n+2)$

Hence, factorised.