Chapter 7 - Polynomial Equations and Factoring - 7.5 - Factoring x 2 + bx + c - Exercises - Page 390: 48

$(x+4y)(x+2y)$

To factor the polynomial $x^{2}+bx+c$ to $(x+p)$ and $(x+q)$, we need to have $p+q=b$ and $pq=c$. Similarly, to factor $x^{2}+6xy+8y^{2}$ to $(x+p)$ and $(x+q)$, we need to have $p+q=6y$ and $pq=8y^{2}$ $\implies p=4y$ and $q=2y$. Then, $x^{2}+6xy+8y^{2}=(x+4y)(x+2y)$