Factorization of (x + y)2+9(x+y)+ 8 is
(x+y+1)(x+y)
(x+y+1)(x+y+8)
(x + y +1)(x + y +6)
(x+y+8)(x+y+2)
Explanation:
$\left(x+y\right)^2+9\left(x+y\right)+8$
$=\left(\left(x+y\right)^2+\left(x+y\right)\right)+\left(8\left(x+y\right)+8\right)$
$=\left(x+y\right)\left(\left(x+y\right)+1\right)+8\left(\left(x+y\right)+1\right)$
$=\left(\left(x+y\right)+1\right)\left(\left(x+y\right)+8\right)$
$=\left(x+y+1\right)\left(x+y+8\right)$
$\left(x+y\right)^2+9\left(x+y\right)+8$
$=\left(\left(x+y\right)^2+\left(x+y\right)\right)+\left(8\left(x+y\right)+8\right)$
$=\left(x+y\right)\left(\left(x+y\right)+1\right)+8\left(\left(x+y\right)+1\right)$
$=\left(\left(x+y\right)+1\right)\left(\left(x+y\right)+8\right)$
$=\left(x+y+1\right)\left(x+y+8\right)$