Chapter 7 - Polynomial Equations and Factoring - 7.5 - Factoring x 2 + bx + c - Exercises - Page 390: 51

$(x-7y)(x+5y)$

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 $x^{2}-2xy-35y^{2}$ to $(x+p)$ and $(x+q)$, we need to have $p+q=-2y$ and $pq=-35y^{2}$ $\implies p=-7y$ and $q=5y$. Then, $x^{2}-2xy-35y^{2}=(x-7y)(x+5y)$